Algebra
# Partial Fractions

Evaluate

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

Evaluate

$\frac{1}{\sqrt{4}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{10}}+\cdots+\frac{1}{\sqrt{397}+\sqrt{400}}.$

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

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