Question

I'm looking for some help on how to determine convergence for this series, I'm thinking I can use the comparison test

Answer 1

\[\sum_{n = 1}^{\infty} \frac{ 2 + \cos^2(n+2) }{ (n+2)^2 }\]

Answer 2

I figured I could try using \[Bn = \frac{ 1 }{ (n+2)^2 }\], which indeed converges, however I googled this one and apparently it is not easy to prove convergence for it.

Answer 3

Well, I was going to suggest that cosine just has a max of 1, but that doesn't help much.

Answer 4

that cosine squared has an upper bound of 6 something

Answer 5

By pythagorean identity, cos^2(n+2)+ sin^2(n+2)=1, so that cos^2 term shouldn't get larger than 1 unless I have it confused by something else, which is completely possible.