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1.5a Lösning 11 - Versionshistorik
2026-06-21T00:39:31Z
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Taifun den 5 september 2014 kl. 12.24
2014-09-05T12:24:44Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.24</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 44:</td>
<td colspan="2" class="diff-lineno">Rad 44:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} = {2 \over 1+\sqrt{5}} + {4 \over (1+\,\sqrt{5})^2} = {2(1+\sqrt{5}) + 4 \over (1+\sqrt{5})^2} = {6+2\,\sqrt{5} \over 1+2\sqrt{5}+5} = {6+2\,\sqrt{5} \over 6+2\sqrt{5}} = 1 </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} = {2 \over 1+\sqrt{5}} + {4 \over (1+\,\sqrt{5})^2} = {2(1+\sqrt{5}) + 4 \over (1+\sqrt{5})^2} = {6+2\,\sqrt{5} \over 1+2\sqrt{5}+5} = {6+2\,\sqrt{5} \over 6+2\sqrt{5}} = 1 </math></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:<math> {1\over r_2} + {1\over r_2^2} = {2 \over 1-\sqrt{5}} + {4 \over (1-\,\sqrt{5})^2} = {2(1-\sqrt{5}) + 4 \over (1-\sqrt{5})^2} = {6-2\,\sqrt{5} \over 1-2\sqrt{5}+5} = {6-2\,\sqrt{5} \over 6-2\sqrt{5}} = 1 </math></ins></div></td></tr>
</table>
Taifun
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Taifun den 5 september 2014 kl. 12.22
2014-09-05T12:22:22Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.22</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 43:</td>
<td colspan="2" class="diff-lineno">Rad 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} = {2 \over 1+\sqrt{5}} + {4 \over (1+\,\sqrt{5})^2} = {2(1+\sqrt{5}) + 4 \over (1+\sqrt{5})^2} = {6+2\,\sqrt{5} \over 6+2\sqrt{5}} = 1 </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} = {2 \over 1+\sqrt{5}} + {4 \over (1+\,\sqrt{5})^2} = {2(1+\sqrt{5}) + 4 \over (1+\sqrt{5})^2<ins class="diffchange diffchange-inline">} = {6+2\,\sqrt{5} \over 1+2\sqrt{5}+5</ins>} = {6+2\,\sqrt{5} \over 6+2\sqrt{5}} = 1 </math></div></td></tr>
</table>
Taifun
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Taifun den 5 september 2014 kl. 12.20
2014-09-05T12:20:21Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.20</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 43:</td>
<td colspan="2" class="diff-lineno">Rad 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} <del class="diffchange diffchange-inline">\,</del>=<del class="diffchange diffchange-inline">\, </del>{2 \over 1<del class="diffchange diffchange-inline">\,</del>+<del class="diffchange diffchange-inline">\,</del>\sqrt{5}} + {4 \over (1<del class="diffchange diffchange-inline">\,</del>+\,\sqrt{5})^2} <del class="diffchange diffchange-inline">\,</del>=<del class="diffchange diffchange-inline">\, </del>{2 <del class="diffchange diffchange-inline">\, </del>(1<del class="diffchange diffchange-inline">\,</del>+<del class="diffchange diffchange-inline">\,</del>\sqrt{5}) + 4 \over (1<del class="diffchange diffchange-inline">\,</del>+<del class="diffchange diffchange-inline">\,</del>\sqrt{5})^2} <del class="diffchange diffchange-inline">\,</del>=<del class="diffchange diffchange-inline">\, </del>{6<del class="diffchange diffchange-inline">\,</del>+<del class="diffchange diffchange-inline">\,</del>2\,\sqrt{5} \over 6<del class="diffchange diffchange-inline">\,</del>+<del class="diffchange diffchange-inline">\,</del>2<del class="diffchange diffchange-inline">\,</del>\sqrt{5}} <del class="diffchange diffchange-inline">\,</del>=<del class="diffchange diffchange-inline">\, </del>1 </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} = {2 \over 1+\sqrt{5}} + {4 \over (1+\,\sqrt{5})^2} = {2(1+\sqrt{5}) + 4 \over (1+\sqrt{5})^2} = {6+2\,\sqrt{5} \over 6+2\sqrt{5}} = 1 </math></div></td></tr>
</table>
Taifun
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Taifun den 5 september 2014 kl. 12.18
2014-09-05T12:18:23Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.18</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 43:</td>
<td colspan="2" class="diff-lineno">Rad 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} \,=\, {2 \over 1\,+\,\sqrt{5}} + {4 \over (1\,+\,\sqrt{5})^2} \,=\, {2 \, (1\,+\,\sqrt{5}) + 4 \over (1\,+\,\sqrt{5})^2} \,=\, {6\,+\,\sqrt{5} \over <del class="diffchange diffchange-inline">(1</del>\,+\,\sqrt{5}<del class="diffchange diffchange-inline">)^2</del>} \,=\, </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} \,=\, {2 \over 1\,+\,\sqrt{5}} + {4 \over (1\,+\,\sqrt{5})^2} \,=\, {2 \, (1\,+\,\sqrt{5}) + 4 \over (1\,+\,\sqrt{5})^2} \,=\, {6\,+<ins class="diffchange diffchange-inline">\,2</ins>\,\sqrt{5} \over <ins class="diffchange diffchange-inline">6</ins>\,+<ins class="diffchange diffchange-inline">\,2</ins>\,\sqrt{5}} \,=\, <ins class="diffchange diffchange-inline">1 </ins></math></div></td></tr>
</table>
Taifun
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Taifun den 5 september 2014 kl. 12.16
2014-09-05T12:16:45Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.16</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 43:</td>
<td colspan="2" class="diff-lineno">Rad 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} \,=\, {2 \over 1\,+\,\sqrt{5}} + {4 \over (1\,+\,\sqrt{5})^2} \,=\, {2 \, (1\,+\,\sqrt{5}) + 4 \over (1\,+\,\sqrt{5})^2} </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} \,=\, {2 \over 1\,+\,\sqrt{5}} + {4 \over (1\,+\,\sqrt{5})^2} \,=\, {2 \, (1\,+\,\sqrt{5}) + 4 \over (1\,+\,\sqrt{5})^2} <ins class="diffchange diffchange-inline">\,=\, {6\,+\,\sqrt{5} \over (1\,+\,\sqrt{5})^2} \,=\, </ins></math></div></td></tr>
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Taifun
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Taifun den 5 september 2014 kl. 12.13
2014-09-05T12:13:12Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.13</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 43:</td>
<td colspan="2" class="diff-lineno">Rad 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} \,=\, {2 \over 1\,+\,\sqrt{5}} + {4 \over( 1\,+\,\sqrt{5})^2} </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} \,=\, {2 \over 1\,+\,\sqrt{5}} + {<ins class="diffchange diffchange-inline">4 \over (1\,+\,\sqrt{5})^2} \,=\, {2 \, (1\,+\,\sqrt{5}) + </ins>4 \over (1\,+\,\sqrt{5})^2} </math></div></td></tr>
</table>
Taifun
https://minidemo.mathonline.se/index.php?title=1.5a_L%C3%B6sning_11&diff=13994&oldid=prev
Taifun den 5 september 2014 kl. 12.09
2014-09-05T12:09:49Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.09</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 43:</td>
<td colspan="2" class="diff-lineno">Rad 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} \,=\, <del class="diffchange diffchange-inline"> </del></math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} \,=\, <ins class="diffchange diffchange-inline">{2 \over 1\,+\,\sqrt{5}} + {4 \over( 1\,+\,\sqrt{5})^2} </ins></math></div></td></tr>
</table>
Taifun
https://minidemo.mathonline.se/index.php?title=1.5a_L%C3%B6sning_11&diff=13993&oldid=prev
Taifun den 5 september 2014 kl. 12.07
2014-09-05T12:07:07Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.07</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 43:</td>
<td colspan="2" class="diff-lineno">Rad 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \; {\rm , \; därför\;att:} </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math> <del class="diffchange diffchange-inline">c_1\:r_1^n\,\left(</del>{1\over r_1} + {1\over r_1^2}<del class="diffchange diffchange-inline">\right) </del>\,<del class="diffchange diffchange-inline">0</del>\,  </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math> {1\over r_1} + {1\over r_1^2} \,<ins class="diffchange diffchange-inline">=</ins>\,  </math></div></td></tr>
</table>
Taifun
https://minidemo.mathonline.se/index.php?title=1.5a_L%C3%B6sning_11&diff=13992&oldid=prev
Taifun den 5 september 2014 kl. 12.05
2014-09-05T12:05:45Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.05</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 41:</td>
<td colspan="2" class="diff-lineno">Rad 41:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> F(n-1) + F(n-2) \,=\, c_1\:r_1^n\,{1\over r_1}\,+\,c_2\:r_2^n\,{1\over r_2}\;+\;c_1\:r_1^n\,{1\over r_1^2}\,+\,c_2\:r_2^n\,{1\over r_2^2} \,=\, </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> F(n-1) + F(n-2) \,=\, c_1\:r_1^n\,{1\over r_1}\,+\,c_2\:r_2^n\,{1\over r_2}\;+\;c_1\:r_1^n\,{1\over r_1^2}\,+\,c_2\:r_2^n\,{1\over r_2^2} \,=\, </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \<del class="diffchange diffchange-inline">quad </del>{\rm , \; därför\;att:} </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \<ins class="diffchange diffchange-inline">; </ins>{\rm , \; därför\;att:} <ins class="diffchange diffchange-inline"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:<math> c_1\:r_1^n\,\left({1\over r_1} + {1\over r_1^2}\right) \,0\,  </ins></math></div></td></tr>
</table>
Taifun
https://minidemo.mathonline.se/index.php?title=1.5a_L%C3%B6sning_11&diff=13991&oldid=prev
Taifun den 5 september 2014 kl. 12.03
2014-09-05T12:03:58Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 5 september 2014 kl. 12.03</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 41:</td>
<td colspan="2" class="diff-lineno">Rad 41:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> F(n-1) + F(n-2) \,=\, c_1\:r_1^n\,{1\over r_1}\,+\,c_2\:r_2^n\,{1\over r_2}\;+\;c_1\:r_1^n\,{1\over r_1^2}\,+\,c_2\:r_2^n\,{1\over r_2^2} \,=\, </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:<math> F(n-1) + F(n-2) \,=\, c_1\:r_1^n\,{1\over r_1}\,+\,c_2\:r_2^n\,{1\over r_2}\;+\;c_1\:r_1^n\,{1\over r_1^2}\,+\,c_2\:r_2^n\,{1\over r_2^2} \,=\, </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1<del class="diffchange diffchange-inline">\,</del>^n\;+\;c_2\:r_2<del class="diffchange diffchange-inline">\,</del>^n \, = \, F(n) \quad {\rm , \<del class="diffchange diffchange-inline">quad </del>därför\;att:} </math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math> \,=\, c_1\:r_1^n\,\left({1\over r_1}+{1\over r_1^2}\right) \,+\, c_2\:r_2^n\,\left({1\over r_2}+{1\over r_2^2}\right) \, = \, c_1\:r_1^n\;+\;c_2\:r_2^n \, = \, F(n) \quad {\rm , \<ins class="diffchange diffchange-inline">; </ins>därför\;att:} </math></div></td></tr>
</table>
Taifun