Let S(n) = 1 + 2 +???..+ n be the sum of the first n natural numbers and let C(n) =13 + 23 + - + n3 be the sum of the first n cubes. Prove the following equalities by induction on n, to arrive at the curious conclusion that C(n) = S ² (n) for every n.

a.

b.

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S(n) = n(n+1). C(n) = (nª + 2n³ + n²) = ¼n²(n + 1)² S(n) = n(n+1). C(n) = (nª + 2n³ + n²) = ¼n²(n + 1)²

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a The sum of the first n natural numbers S n 1 2 3 n is given by Hence induction method is us... View the full answer