• Jun 11th 2010, 10:01 AM
moonnightingale
$\sum_{n=0}^\infty ar^n= \frac{a}{1- r}$.
Now, the derivative, term by term, is $\sum_{n=0}^\infty a_n r^{n-1}$ and that must be equal to the derivative, with respect to r, of $\frac{a}{1- r}$.