Telescoping Series 5 – Introducing The Telescope

Given the following, evaluate $\frac{1}{1\times2} + \frac{1}{2\times3} + \frac{1}{3\times4}$:

$\begin{array}{lllll} & \frac{1}{1\times2}= & \frac{1}{1} & - \frac{1}{2} & &\\ & \frac{1}{2\times3}= & &+ \frac{1}{2} & - \frac{1}{3} & \\ + & \frac{1}{3\times4}=& & & + \frac{1}{3} & - \frac{1}{4} \\ \hline \end{array}$