Is there any way to prove that: $$ 1^2+2^2+3^2+\ldots +n^2=\frac{n(n+1)(2n+1)}{6}$$ but WITHOUT using mathematical induction? (I don't know, maybe through some creative graphical demonstration?)
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$f(n) = \frac{n(n+1)(2n+1)}{6}, f(n)-f(n-1) = n^2, f(0) = 0$ – reuns Mar 24 '17 at 11:08
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Yes, there is a graphic proof by Man-Keung Siu, appeared in: Mathematics Magazine March, 1984
Erel Segal-Halevi
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