estimate error of partial sum, terms too complex to integrate

Hi all,

The problem is to calculate this sum to 10 terms and estimate the error:

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

I summed the first 10 terms, no problem.

If I understand correctly, the error is less than

$\displaystyle \int_{10}^{\infty} \frac{n}{(n+1)3^n} dn$

but I can't figure out how to integrate that. I have the feeling that I can just use

$\displaystyle \int_{10}^{\infty} \frac{1}{3^n} dn$

to approximate my error, but it seems like I need to say more to justify this.. Or maybe I'm just missing the integration technique for the more complex form.

Thanks again for any help!

Brian