..., 98, 99, 100!

Algebra Level 2

\( \begin{align} S &= \frac {1}{90\times 91} + \frac {1}{91\times 92} + \frac {1}{92\times 93} + \frac {1}{93\times 94} \\ & + \frac {1}{94\times 95} + \frac {1}{95\times 96} + \frac {1}{96\times 97} + \frac {1}{97\times 98} \\ & + \frac {1}{98\times 99} + \frac {1}{99\times 100}\\ \end{align} \)

If \( S = \frac {a}{b} \), where \(a\) and \(b\) are coprime positive integers, what is the value of \(a+b\)?

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