Converge?

Algebra Level 2

Let S\Large{S} = 11.2+12.3+..........+199.100\dfrac{1}{1.2} + \dfrac{1}{2.3} + .......... + \dfrac{1}{99.100}

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

Find bab-a.

NOTE -: a.b=a×ba.b = a \times b

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