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: (a) S(n) = 1/2*n(n + 1). (b) C(n) = 1/4*(n^4 + 2n^3 + n^2) = 1/4*n^2(n + 1)^2.

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