\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{5}\right)\cdot...\cdot\left(1-\dfrac{1}{x}\right)=\dfrac{1}{100}\)
\(\Leftrightarrow\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot...\cdot\dfrac{x-1}{x}=\dfrac{1}{100}\)
\(\Leftrightarrow x=100\)