1. Express

   $$\frac{1}{r(r+1)}$$

   in partial fractions.

2. Hence, or otherwise, find the value of

   $$\sum _{r=1}^{99}\frac{1}{r^2+r}$$

For part (a), you need

For part (b), write the function in partial fractions and then try working out $S_2$ and $S_3$. A lot of terms in the sum can cancel making it very easy to calculate.