By expressing $\frac{1}{(4r-1)(4r+3)}$ in partial fractions, evaluate $\sum\limits_{r=1}^{n}{\frac{1

Question

By expressing $\frac{1}{(4r-1)(4r+3)}$ in partial fractions, evaluate $\sum\limits_{r=1}^{n}{\frac{1}{(4r-1)(4r+3)}}$.

Accepted Answer

$\frac{1}{4}\left[\frac{1}{3} - \frac{1}{4n+3}\right]$

Worked Example 3