Determine the convergence of ∑n=1∞cos2(n)n2\sum_{n=1}^{\infty} \frac{\cos^2(n)}{n^2}∑n=1∞n2cos2(n).
Converges by Comparison Test with ∑1n2\sum \frac{1}{n^2}∑n21.
Diverges because cos2(n)\cos^2(n)cos2(n) oscillates.
Converges by Ratio Test.
Diverges by ppp-series test.