Sum function of power series ∑ (n = 1 to ∞) [(- 1) ^ (n-1) / (n + 1)] (x-1) ^ n What if n = 0

The convergence domain is (0,2]. Multiply X-1 to get the derivative, and then integrate, [(x-1) s (x)] '= ∑ (- 1) ^ (n-1) (x-1) ^ n = (x-1) ∑ (1-x) ^ (n-1) = (x-1) × 1 / (1 - (1-x)) = (x-1) / x = 1-1 / X (x-1) s (x) = x-lnx-1s (x) = 1-lnx / (x-1), 0 < x ≤ 2

What is the sum function of power series ∑ (- x) ^ n in (- 1,1)

If n goes from 0 to infinity: = 1 / (1 + x)

The function f (x) = 1 / (x + 2) is expanded into a power series of X-1

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