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 \(b-a\).
by
Jake Lai