Suppose 0 k f(x) = and g(x)=k(k+3)xk. k + 7 k=0 k=0 For any for...

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Suppose ∞0 k f(x) = Σ and g(x)=k(k+3)xk. k + 7 k=0 k=0 For any for which both series converge, define h(x) = (2x - 7)f(x) + 6x²g(x). For these x, find the power series for h(x). h(x) = 3 || C₁ = Ck = k=0 Ckak. for k > 2. Note: co and c₁ should be numbers, C for k2 should be a function of k. Suppose ∞0 k f(x) = Σ and g(x)=k(k+3)xk. k + 7 k=0 k=0 For any for which both series converge, define h(x) = (2x - 7)f(x) + 6x²g(x). For these x, find the power series for h(x). h(x) = 3 || C₁ = Ck = k=0 Ckak. for k > 2. Note: co and c₁ should be numbers, C for k2 should be a function of k.