The value of \(\left(1 + \frac{1}{2}\right) \left( 1 + \frac{1}{3} \right) \cdots \left( 1 + \frac{1}{100}\right)\) can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a +b?\)

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