https://artofproblemsolving.com/wiki/index.php?title=2006_UNCO_Math_Contest_II_Problems/Problem_6&feed=atom&action=history
2006 UNCO Math Contest II Problems/Problem 6 - Revision history
2024-03-28T14:16:14Z
Revision history for this page on the wiki
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Timneh: /* Solution */
2019-01-13T06:33:23Z
<p><span dir="auto"><span class="autocomment">Solution</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 06:33, 13 January 2019</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; 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>{{<del class="diffchange diffchange-inline">solution</del>}}</div></td><td class='diff-marker'>+</td><td style="color: #222; 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">(a) <math>\frac</ins>{<ins class="diffchange diffchange-inline">(2^</ins>{<ins class="diffchange diffchange-inline">n+1</ins>}<ins class="diffchange diffchange-inline">-1)(3^{n+1}-1)}{2}</math> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; 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: #222; 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">(b) <math>\frac{(2^{2n+1}-1)(3^{n+1}-1)}{2</ins>}<ins class="diffchange diffchange-inline"></math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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Timneh
https://artofproblemsolving.com/wiki/index.php?title=2006_UNCO_Math_Contest_II_Problems/Problem_6&diff=81836&oldid=prev
Mathisfun04: /* Solution */
2016-12-09T21:58:06Z
<p><span dir="auto"><span class="autocomment">Solution</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 21:58, 9 December 2016</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td></tr>
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Mathisfun04
https://artofproblemsolving.com/wiki/index.php?title=2006_UNCO_Math_Contest_II_Problems/Problem_6&diff=65360&oldid=prev
Timneh: Created page with "== Problem == The sum of all of the positive integer divisors of <math>6^2=36</math> is <math>1+2+3+4+6+9+12+18+36=91</math> (a) Determine a nice closed formula (i.e. without ..."
2014-10-21T07:12:43Z
<p>Created page with "== Problem == The sum of all of the positive integer divisors of <math>6^2=36</math> is <math>1+2+3+4+6+9+12+18+36=91</math> (a) Determine a nice closed formula (i.e. without ..."</p>
<p><b>New page</b></p><div>== Problem ==<br />
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The sum of all of the positive integer divisors of <math>6^2=36</math> is <math>1+2+3+4+6+9+12+18+36=91</math><br />
<br />
(a) Determine a nice closed formula (i.e. without dots or the summation symbol) for the sum of all positive divisors of <math>6^n</math>.<br />
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(b) Repeat for <math>12^n</math>.<br />
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(c) Generalize.<br />
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==Solution==<br />
<br />
==See Also==<br />
{{UNCO Math Contest box|n=II|year=2006|num-b=5|num-a=7}}<br />
<br />
[[Category:Introductory Algebra Problems]]</div>
Timneh