Visual/intuitive proof of why $\sum k^3 = (\sum k)^2$, where $k$ goes from 1 to $n$?

Asked Apr 19 '13 at 20:13

Active Apr 19 '13 at 20:17

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I understand that one could prove this by first proving the analytic expressions of the sigma terms through induction, and then square the $\displaystyle\sum_{k=1}^n k$ term to show LHS = RHS.

Are there any other easier to understand (preferably visual) proofs one could show?

Thanks.

edited Apr 19 '13 at 20:17

George V. Williams

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asked Apr 19 '13 at 20:13

JDS

Have you looked here? – L. F. Apr 19 '13 at 20:17
This is also worth a look. – Old John Apr 19 '13 at 20:19

Visual/intuitive proof of why $\sum k^3 = (\sum k)^2$, where $k$ goes from 1 to $n$?

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