\[ \large \frac12 \cdot\frac23 \cdot \frac34 \cdot\frac45 \cdot \ldots \cdot x = \frac1{100} \]

Above shows the product of \(x\) fractions such that its product equals to \(\frac{1}{100} \). If each of these \(x\) fractions have their numerator is 1 less than its denominator, find the value of \(x\).

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