How do I compute $ \sum\limits_{n=0}^{\infty} \frac{1}{(n+2)7^n} $? I'm trying to evaluate the following sum:
$$ \sum\limits_{n=0}^{\infty} \frac{1}{(n+2)7^n} $$
Probably the best way to do that is to try and find a closed formula for 
$$ \sum\limits_{n=0}^{\infty}  \frac{1}{(n+2)x^n} $$
Probably it requires some integrating/differentiating. I've tried both, but I can't get it to look any more decently.
I'd appreciate some hint

This Taylor series should help you: $$\ln(1-x) = -\sum_{n=1}^{\infty}\frac{x^{n}}{n}, \ \ |x| < 1$$
