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How do you evaluate the sum of the series:-

(1^2) + (2^2)+.....(k^2) ?

I do know how to prove that the sum is k(k+1)(2k+1)/6 by induction, but I'm just curious: how do you figure out the pattern for this, and other similar summation series?

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# Sum of 1^2 +2^2 +.k^2

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