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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 **\(b-a\)**?

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