Limit of $\frac{1}{a} + \frac{2}{a^2} + \cdots + \frac{n}{a^n}$ What is the limit of this sequence $\frac{1}{a} + \frac{2}{a^2} + \cdots + \frac{n}{a^n}$?
Where $a$ is a constant and $n \to \infty$.
If answered  with proofs, it will be best. 

Hint:
$\frac{1}{a} + \frac{2}{a^2} + \cdots + \frac{n}{a^n}$ = $(\frac{1}{a} + \frac{1}{a^2} + \cdots + \frac{1}{a^n}) + (\frac{1}{a^2} + \frac{1}{a^3} + \cdots + \frac{1}{a^n}) + ...$ 
Simplify each sum, factor out common terms and it will become more clear to solve. :)
