# Inverse summation

Calculus Level 4

If $$\displaystyle \sum_{n=1}^{\infty}\cot^{-1}\left(\frac{2}{1729}+\frac{(n+n^{2})1729}{2} \right)=\tan^{-1}\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, then what is the value of $$a+b$$?

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