1. ## Another series problem

Hi,

I want to see if this series is convergent but I'm a bit lost.

\sum_{n = 1}^\infty (5 - 2cos n)/(3n^3 + n + 2).

Obviously it's dominated by 1/n^3, and i'm sure it is convergent, but I'm struggling to manipulate the expression to prove this. Any advice on how to get going?

Thanks.

2. Since $|5-2\cos n|\leq 5+2=7$ and $3n^3+n+2\geq 3n^3$, we get $\left|\frac{5-2\cos n}{3n^3+n+2}\right|\leq \frac 7{3n^3}$.
It's not dominated by $\frac 1{n^3}$ but by something with the form $\frac C{n^3}$.

3. I would never have thought of solving it that way but it makes sense. Thanks for your help Girdav.