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132+1+142+2+152+3 +162+4 +⋯ \large \frac{1}{3^2+1} +\frac{1}{4^2 +2}+ \frac{1}{5^2+3}\ + \frac{1}{6^2+4}\ + \cdots 32+11+42+21+52+31 +62+41 +⋯
The series above can be expressed as mn \dfrac mnnm, where mmm and nnn are coprime positive integers.
Find m+nm+nm+n.
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