Use induction to prove \sum_{i=0}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}
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Inductive step: Assume that the statement is true for some arbitrary positive integer k, i.e., k(k+1)(2k+1) = 2k^3 + 3k^2 + k. We want to show that the statement is also true for k+1, i.e., (k+1)(k+2)(2k+3) = 2(k+1)^3 + 3(k+1)^2 + (k+1). Expanding the left-hand Show more…
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