Answer
See the proof below.
Work Step by Step
We have
$$
\sum_{n=0}^{\infty} \frac{9^{n}+2^{n}}{5^{n}}=\sum_{n=0}^{\infty} \frac{9^{n}}{5^{n}}+\sum_{n=0}^{\infty} \frac{2^{n}}{5^{n}}
$$
One can see that the series $\sum_{n=0}^{\infty} \frac{9^{n}}{5^{n}}$ is a geometric series with $r=\frac{9}{5}\gt 1$. Thus, it is divergent and hence the given series is divergent.
