Answer
The series $\sum_{n=1}^{\infty} ne^{-0.02n}$ converges.
Work Step by Step
We apply the ratio test as follows, $a_n=ne^{-0.02n}$
$$
\rho=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right|=\lim _{n \rightarrow \infty}\frac{(n+1)e^{-0.02}}{n}\\
=\lim _{n \rightarrow \infty}(1+(1/n))e^{-0.02}=e^{-0.02}=0.98\lt 1
$$
Hence the series $\sum_{n=1}^{\infty} ne^{-0.02n}$ converges.
