Question

Sigma n=1 to infinity (-1)^n sin(1/n)

Answer 1

This is an alternating series. We shall use alternating series test to check if it converges or not.

$\lim_{n\to \infty}\sin(\frac{1}{n})=\sin(0)=0$

Hence, the series $\sum_{n=1}^{\infty} (-1)^n \sin(\frac{1}{n})$ is convergent by the alternating series test.