CPM Homework Help : CALC Problem 11-49

Multiple Choice: The interval of convergence of the power series $\displaystyle\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { x ^ { n } } { n }$ is:

$(−∞,∞)$

$[−1,1]$

$[−1,1)$

$(−1,1]$

$(−1,1)$

Use the Ratio Test.

$\lim_{n\to\infty}|x|\cdot\frac{n}{n+1}=$

If x = –1:

$\sum_{n=1}^{\infty}(-1)^{n-1}\frac{(-1)^n}{n}=\sum_{n=1}^{\infty}\frac{(-1)^{2n-1}}{n}=\sum_{n=1}^{\infty}(-1)^{n-1}\frac{(-1)}{n}$

Does this resultant series converge or diverge?
Be sure to check the resultant series if x = 1.