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Given the following, evaluate 11×2+12×3+13×4 \frac{1}{1\times2} + \frac{1}{2\times3} + \frac{1}{3\times4}1×21+2×31+3×41:
11×2=11−1212×3=+12−13+13×4=+13−14 \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}+1×21=2×31=3×41=11−21+21−31+31−41
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