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Let αn,βn\alpha_{n}, \beta_{n}αn,βn be the distinct roots of the equation x2+(n+1)x+n2=0x^{2}+(n+1)x+n^{2} = 0x2+(n+1)x+n2=0. If
∑n=220151(αn+1)(βn+1)\sum_{n=2}^{2015} \frac{1}{(\alpha_{n}+1)(\beta_{n}+1)}n=2∑2015(αn+1)(βn+1)1
can be expressed in the form ab\frac{a}{b}ba, where aaa and bbb are positive coprime integers, find b−ab-ab−a.
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