Mathematics

Mathematics

Problem

The series representation 11+t=∑n=0∞(−1)ntn\displaystyle \frac{1}{1+t}=\sum_{n=0}^{\infty}(-1)^{n}t^{n} holds for ∣t∣<1|t|<1. Integrating term-by-term from t=0t=0 to t=xt=x produces a series for ln⁡(1+x)\ln(1+x). On which of the following intervals does this new series converge? a) ∣x∣<1|x|<1 b) x>−1x>-1 c) −1<x≤1-1<x\le 1 d) ∣x∣≤1|x|\le 1

Browse the problem library