Telescopic summation

Algebra Level 3

\[ \large \frac{1}{3^2+1} +\frac{1}{4^2 +2}+ \frac{1}{5^2+3}\ + \frac{1}{6^2+4}\ + \cdots \]

The series above can be expressed as \( \dfrac mn\), where \(m\) and \(n\) are coprime positive integers.