Question 0519

By writing ${\displaystyle \frac{1}{4 r^2 - 1}}$ in partial fractions, find an expression for ${\displaystyle \sum_{r=1}^n \frac{1}{4 r^2 - 1}.}$

Hence find the exact value of ${\displaystyle \sum_{r=8}^\infty \frac{1}{4 r^2 - 1}.}$