Originally Posted by

**Laban** Well, in class we were shown that $\displaystyle \sum\limits_{n = 1}^\infty {nx^n } = \frac{x}{{\left( {1 - x} \right)^2 }}$.

and you say that $\displaystyle \sum\limits_{n = 0}^\infty {nx^n } = \frac{x}{{\left( {1 - x} \right)^2 }}$.

so is true to say that $\displaystyle \sum\limits_{n \geq 0}^\infty {nx^n } = \frac{x}{{\left( {1 - x} \right)^2 }}$ ?

If so, just out of curiosity, how is it same for all $\displaystyle n \geq 0$?

and if it's not true, what would be the case for n = 2 ?