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1. Find the radius of convergence for: ∞∑n=1 (−1)^n x^n / √n+9 2. If f(x)=∞∑n=0 n...

1. Find the radius of convergence for:
∞∑n=1 (−1)^n x^n / √n+9

2. If f(x)=∞∑n=0 n /n^2+1 x^n and g(x)=∞∑n=0 (−1)^n n /n^2+1 x^n, find the power series of 1/2(f(x)+g(x)).
∞∑n=0 =

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