Answer
Convergent
Work Step by Step
Apply the comparison test.
$\frac{2 + (−1)^{k}}{5^{k}}\leq\left(\frac{3}{5}\right)^{k}$
Since the series $\sum \left(\frac{3}{5}\right)^{k}$ is a geometric series with ratio $\left|\frac{3}{5}\right|<1$, which is convergent, it follows that the given series is also convergent.
