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Let S\Large{S}S = 11.2+12.3+..........+199.100\dfrac{1}{1.2} + \dfrac{1}{2.3} + .......... + \dfrac{1}{99.100}1.21+2.31+..........+99.1001
S\Large{S}S can be expressed as ab\frac{a}{b}ba, where a,ba,ba,b are co-prime integers.
Find b−ab-ab−a.
NOTE -: a.b=a×ba.b = a \times ba.b=a×b
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