# Thread: Are these series convergent?

1. ## Are these series convergent?

Hi there,

I need a little help with testing the following series for convergence:

\sum_{n = 1}^\infty (7 - 4n + 5n^3)/(2n^3 - 6n + 3)

I'm sure this is very basic and doesn't involve using the limit comparison test or the ratio test but although i know it's a convergent sequence, it's just not obvious to me how to solve it. I'd appreciate any help pointing me in the right direction.

Thanks.

2. Compute the limit of the term you have to sum.

3. A necessary condition for a series to be convergent is that $\displaystyle \lim_{n \to \infty}a_n = 0$.

So a basic test for divergence is to evaluate $\displaystyle \lim_{n \to \infty}a_n$ and show that it $\displaystyle \neq 0$.

4. Yes, I get it now! Thanks for the help guys.