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Automata Please prove the following by induction. Let S(n) be the sum of squares from 1...

Automata

Please prove the following by induction. Let S(n) be the sum of squares from 1 to n, i.e., S(n)=1^2 + 2^2 + 3^2 + ... + n^2 Then S(n) = n(n+1)(2n+1)/6 = (2n^3+3n^2+n)/6

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