# Telescoping Series 2 – Future Terms

Algebra Level 2

Consider the following pattern:

\begin{align} \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{align}

Following the pattern above, if $$\displaystyle \frac{1}{11\times 12} = \frac{1}{a} - \frac{1}{b},$$ what are the values of $$a$$ and $$b$$?

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