# How do you test the series sum_(n=1)^(oo) sin^2n/n^2 for convergence?

Mar 10, 2018

Converges.

#### Explanation:

Recall the series

${\sum}_{n = 1}^{\infty} \frac{1}{n} ^ 2$

By the p-series test, we know that it converges.

Because ${\sin}^{2} n < 1$ for all values of $n$, by the comparison test, we can confirm that this series converges as well.

Hopefully this helps!