# How do I reciprocate a polynomial?

Algebra Level 3

$\large \displaystyle \sum_{n=1}^{2015} \dfrac{1}{T_{n}}$

If $$T_{n} = \frac{1}{4} (n+2)(n+3)$$, the value of the above sum is in the form $$\dfrac{A}{B}$$, where $$A,B \in \mathbb{N}$$ and $$\gcd(A,B)=1$$. Find $$A+B$$.

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