# Sum of roots with a twist

Calculus Level 3

Let $$\alpha_{n}, \beta_{n}$$ be the distinct roots of the equation $$x^{2}+(n+1)x+n^{2} = 0$$. If

$\sum_{n=2}^{2015} \frac{1}{(\alpha_{n}+1)(\beta_{n}+1)}$

can be expressed in the form $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers, find $$b-a$$.

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