Power sums/Induction/Exercise

Prove the following formulas by induction.

1. Failed to parse (syntax error): {\displaystyle {{}} \sum_{i <table class="metadata plainlinks ambox ambox-notice" style=""> <tr> <td class="mbox-image"><div style="width: 52px;"> [[File:Wikiversity logo 2017.svg|50px|link=]]</div></td> <td class="mbox-text" style=""> '''[[m:Soft redirect|Soft redirect]]'''<br />This page can be found at <span id="SoftRedirect">[[mw:Help:Magic words#Other]]</span>. </td> </tr> </table>[[Category:Wikiversity soft redirects|Power sums/Induction/Exercise]] __NOINDEX__ 1}^n i = \frac{n(n+1)}{2} \, , }

2. Failed to parse (syntax error): {\displaystyle {{}} \sum_{i <table class="metadata plainlinks ambox ambox-notice" style=""> <tr> <td class="mbox-image"><div style="width: 52px;"> [[File:Wikiversity logo 2017.svg|50px|link=]]</div></td> <td class="mbox-text" style=""> '''[[m:Soft redirect|Soft redirect]]'''<br />This page can be found at <span id="SoftRedirect">[[mw:Help:Magic words#Other]]</span>. </td> </tr> </table>[[Category:Wikiversity soft redirects|Power sums/Induction/Exercise]] __NOINDEX__ 1}^n i^2 = \frac{n(n+1)(2n+1)}{6} \, . }

3. ${}\sum _{i=1}^{n}i^{3}={\left({\frac {n(n+1)}{2}}\right)}^{2}\,.$

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