Converge?

Algebra Level 2

Let $\Large{S}$ = $\dfrac{1}{1.2} + \dfrac{1}{2.3} + .......... + \dfrac{1}{99.100}$

$\Large{S}$ can be expressed as $\frac{a}{b}$ , where $a,b$ are co-prime integers.

Find $b-a$ .

NOTE -: $a.b = a \times b$