Question

Please help me find the interval of convergence of the given power series. (click to see)

Answer 1

\[\sum_{n=1}^{\infty} \frac{ (-1)^{n} }{ n }x ^{n}\]

Answer 2

@abb0t

Answer 3

Use the ratio test:
\[\lim_{n\to\infty}\left|\frac{(-1)^{n+1}x^{n+1}}{n+1}\cdot\frac{n}{(-1)^nx^n}\right|=\lim_{n\to\infty}\frac{n}{n+1}|x|\]
A series converges by the ratio test if this limit is less than 1.