Let ${\alpha }_n,{\beta }_n$ be the distinct roots of the equation $x^2+(n+1)x+n^2=0.$ If $\sum _{n=2}^{2021}\frac{1}{({\alpha }_n+1)({\beta }_n+1)}$ can be expressed in the form $\frac{a}{b},$ Where $a$ and $b$ are positive  integers relatively prime to each other, then the value of $\left(b-a\right)$ is