Wednesday, May 2, 2018

calculus - Derive $sum i^2$ without knowing the answer first

Standard proof that $\sum_1^n i^2=\frac{n(n+1)(2n+1)}{6}$ is given by induction. It is of course a valid method. However, I find that it requires me to memorize the answer. Is there any way I can sit in an exam and just derive the result from scratch without memorization?




This question is apparently more general and different than Gaussian proof for the sum of squares?
and I have seen quite a few great answers other than the "Gaussian method" in the post

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