Thursday, 24 March 2016

Prove that $(sum_{i=1}^n i)^2$ = $sum_{i=1}^n i^3$ by induction

Prove that: $(\sum_{i=1}^n i)^2$ = $\sum_{i=1}^n i^3$




I can use the fact that $\sum_{i=1}^n i$ = n(n+1)/2 after the inductive hypothesis is invoked.
I'm not sure where to start, I would usually break down one side but there isn't usually two sums, so I'm not sure.

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