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

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