I have stumbled on the equality $[\sum i]^2 = \sum i^3$ which holds when both sums are over the range 1 to k. The equality is readily demonstrated inductively, but I wonder if anyone can provide an algebraic proof?
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3I don't understand what you mean with algebraic proof. – Git Gud Jul 13 '13 at 16:31
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The proof by Babak S to the question I inadvertently duplicated ("Proving the identity ...") is what I was looking for. Thanks to all for helping me find it. – Keith Backman Jul 13 '13 at 16:52