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Apply term-wise integration to the expansion 1/(1 − x) = ∑∞ n=0 x n = 1...

Apply term-wise integration to the expansion 1/(1 − x) = ∑∞ n=0 x n = 1 + x + x^2 + x^3 + ... to prove that for −1 < x < 1, − ln(1 − x) = ∑∞ n=0 (x^n+1)/(n + 1) = x + x^2/2 − x^3/3 + x^4/4 + ... You should find a constant that appears when you integrate. (b) Study convergence of this new series at the end points of the interval (−1, 1). (c) Indicate for what values of x the series converges absolutely, conditionally, or not at all.

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