(a) Use differentiation to find a power series representation for f(x) = f(x) = ((-1)n(n+1) 2...

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(a) Use differentiation to find a power series representation for f(x) = f(x) = ((-1)n(n+1) 2 2) - 2² (5(n+ 2)) OF) n=0 What is the radius of convergence, R? R = 5 1 (5 + x)² f(x) = (b) Use part (a) to find a power series for 1 (5 + x)³ 08 n=0 f(x) = ((-1)(n+1)(n+2) What is the radius of convergence, R? R = 5 (xn) 57 +3 OF) (c) Use part (b) to find a power series for f(x) = = f(x) = Σ n=0 R What is the radius of convergence, R? (5 + x)³ 5 (a) Use differentiation to find a power series representation for f(x) = f(x) = ((-1)n(n+1) 2 2) - 2² (5(n+ 2)) OF) n=0 What is the radius of convergence, R? R = 5 1 (5 + x)² f(x) = (b) Use part (a) to find a power series for 1 (5 + x)³ 08 n=0 f(x) = ((-1)(n+1)(n+2) What is the radius of convergence, R? R = 5 (xn) 57 +3 OF) (c) Use part (b) to find a power series for f(x) = = f(x) = Σ n=0 R What is the radius of convergence, R? (5 + x)³ 5

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