(a) Prove that () = 1, (n) = 1, and (^)= (₁ = ¹) + n if 1≤k ≤n-1. (b) Use part (a) and induction to prove that (2) is a positive integer for all n, k = Z such that 0≤ k ≤n. (c) Let x, y E R. Prove that for every integer n ≥ 0, n (x + y)² = Σ (1) xn-kyk, k=0

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