# Thread: Convergence of series

1. ## Convergence of series

Hi,

$\displaystyle \sum_{n=1}^\infty \frac{n+2}{n^3 +1}$

I tried using the ratio test (ended up with 1 so wasn't helpful), similarly the nth root test and integral comparison test didn't work.

Can I say that:

$\displaystyle \frac{n+2}{n^3 +1} \leq \frac{1}{n^2}$

and 1/n^2 converges by the integral comparison test, so by the comparison theorem, the sum converges?

Is the above correct? Thanks

edit: I couldn't get the Latex to work so I've taken off the tags, sorry!

2. ## Re: Convergence of series

try the limit comparison test with the known convergent series $\displaystyle \sum \frac{1}{n^2}$

3. ## Re: Convergence of series

Hi

To use LaTeX put (TEX)(/TEX) tags around the text you want texified except that you shoul put [ instead of ( and ] instead of ) .

4. ## Re: Convergence of series

Thanks for the help. That's what I did, I just wasn't sure if it was right. Thank you!

When I put the tags around it comes up like this $\displaystyle \sum_{n=1}^\infty \frac{n+2}{n^3 +1}$

edit: it's working now! but I literally just copied and pasted form my original post! I'll try again.

5. ## Re: Convergence of series

Originally Posted by Ant
Thanks for the help. That's what I did, I just wasn't sure if it was right. Thank you!

When I put the tags around it comes up like this $\displaystyle \sum_{n=1}^\infty \frac{n+2}{n^3 +1}$

edit: it's working now! but I literally just copied and pasted form my original post! I'll try again.
Simple comparison works.
$\displaystyle \sum_{n=1}^\infty \frac{n+2}{n^3 +1}\le \sum_{n=1}^\infty \frac{2}{n^2 }$