Geometric summation question

Question

Differentiate both sides of the geometric sum with respect to $r$.$$\sum_{i=0}^n r^i = \frac{1-r^{n+1}}{1-r}$$ Use the result to show that $$\sum_{i=1}^n ir^i < \frac{r}{(1-r)^2} \text{ for all } n\ge1 .$$