Answer
Convergent
Work Step by Step
$\Sigma_{n=1}^{\infty}a_{n}=\Sigma_{n=1}^{\infty}\frac{(-1)^{n}}{coshn}$
Note that $a_{n}=\frac{1}{coshn}$ is monotonically decreasing.
This is because $coshn$ is monotonically increasing for $n\gt 0$
Thus the given series is convergent.
