Problem

Part I Multiple Choice

(a) The series $\displaystyle\sum_{n=1}^{\infty} n\cos(n\pi)\sin\frac{1}{n}$ is absolutely convergent.

(b) The series $\displaystyle\sum_{n=1}^{\infty}\sin(n)\frac{n^2+1}{5^n}$ is absolutely convergent.

(c) The series $\displaystyle\sum_{n=2}^{\infty}\frac{(-1)^n}{n(\ln n)^{\sqrt{2}-1}}$ is absolutely convergent.

Among the above three statements, how many of them are true?

A) Only one.

B) Only two.

C) All of them.

D) None of them.