# Behold! Alpha and Beta are on their way!

Level pending

Let $$\alpha_{n}$$ and $$\beta_{n}$$ be the roots of

$x^2+(2n+1)x+n^2$

The sum of

$\frac{1}{(\alpha_{3}+1)(\beta_{3}+1)}+\frac{1}{(\alpha_{4}+1)(\beta_{4}+1)}+\ldots+\frac{1}{(\alpha_{20}+1)(\beta_{20}+1)}$

can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers.

What is the value of $$b-a$$?

×