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 -: \(a.b = a \times b\)

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