I came across the following video on youtube where a kid was asked to show that $\sum_{n = 1}^{\infty} \frac{\sin{(2n)}}{1 + \cos^4{n}}$ is convergent. He tried to use the integral test but wasn't allowed to finish his argument. I have two questions.
(1) Can you apply integral test in this situation since it is not clear if the terms of the series are decreasing?
(2) How do you solve this problem?
