How to prove the series $\sum_{k=1}^\infty k^2\sin^2\left(\frac2k\right)$ converges?

Question

How to prove this series is converging? $$\sum_{k=1}^\infty k^2\sin^2\left(\frac2k\right)$$ Thank you so much!

Answer 1

Note that

$$k^2\sin^2\left(\frac2k\right)\sim4$$

thus it can't converge.