Question: Let S(n) = 1 + 2 +???..+ n be the sum of the first n natural numbers and let C(n) =13 + 23 + -

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.

S(n) = n(n+1). C(n) = (n + 2n + n) = n(n

+ 1)

S(n) = n(n+1). C(n) = (n + 2n + n) = n(n + 1)

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