Question

Test the series for convergence:

Answer 1

\[\sum_{n=1}^{\infty} \frac{2 \sqrt n + 1} {n^2 + n + 1}\]
All method's I've tried yield no results.

Answer 2

http://www.wolframalpha.com/input/?i=sum+%282sqrtn%2B1%29%2F%28n^2%2Bn%2B1%29%2C+n%3D1+to+infinity

Answer 3

That doesn't count on a test, therefore I cannot use that.

Answer 4

Figured it out. Used limit comparison with\[\frac {3} {n^{3/2}}\]

Answer 5

I was working on it..