Question 0519

By writing ${\displaystyle \frac{1}{r^2 - 1}}$ in partial fractions, find an expression for ${\displaystyle \sum_{r=2}^n \frac{1}{r^2 - 1}.}$

Hence find the exact value of ${\displaystyle \sum_{r=13}^\infty \frac{1}{r^2 - 1}.}$