Let S(n) = 1 + 2 + + n be the sum of the rst n natural
Chapter , Problem 0.11(choose chapter or problem)
Let S(n) = 1 + 2 + + n be the sum of the rst n natural numbers and let C(n) = 13 + 23 + + n3 be the sum of the rst n cubes. Prove the following equalitiesby induction on n, to arrive at the curious conclusion that C(n) = S2(n) for every n. a. S(n) = 1 2n(n + 1). b. C(n) = 1 4(n4 + 2n3 + n2) = 1 4n2(n + 1)2.
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