Answer
The series $\sum_{n=2}^{\infty} \frac{n}{1+100n}$ diverges.
Work Step by Step
We have
$$\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \frac{n}{1+100n}=\frac{1}{100}\neq 0.$$
Hence the series $\sum_{n=2}^{\infty} \frac{n}{1+100n}$ diverges.
