Telescoping Series 1 – Find The Next Term

Algebra Level 1

Consider the following pattern:

11×2=111212×3=121313×4=1314\begin{aligned} \frac{1}{1\times 2} & = \frac{1}{1} - \frac{1}{2} \\ & \\ \frac{1}{2\times 3} & = \frac{1}{2} - \frac{1}{3} \\ & \\ \frac{1}{3\times 4} & = \frac{1}{3} - \frac{1}{4} \\ \vdots & \end{aligned}

Following the pattern above, if 14×5=1a1b, \displaystyle \frac{1}{4\times 5} = \frac{1}{a} - \frac{1}{b}, what are the values of a a and b b?

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