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# Partial Fractions

Express rational functions as a sum of fractions with simpler denominators. You can apply this to telescoping series to mass cancel terms in a seemingly complicated sum.

Evaluate

\[\frac{1}{4\cdot10}+\frac{1}{10\cdot16}+\frac{1}{16\cdot22}+\frac{1}{22\cdot28}+\frac{1}{28\cdot34} . \]

If \(f(x)=4x^2-1,\) what is the value of

\[\frac{1}{f(1)}+\frac{1}{f(2)}+\frac{1}{f(3)}+\cdots+\frac{1}{f(84)}?\]

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