`#3107.101107`
\(\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{4}{5}\times\dfrac{5}{6}\times\dfrac{6}{7}\times...\times\dfrac{98}{99}\times\dfrac{99}{100}\)
\(=\left(\dfrac{1}{2}\times\dfrac{2}{3}\right)\times\dfrac{4}{5}\times\dfrac{5}{6}\times\dfrac{6}{7}\times...\times\dfrac{98}{99}\times\dfrac{99}{100}\)
\(=\dfrac{1}{3}\times\dfrac{4}{100}\)
\(=\dfrac{4}{300}\\ =\dfrac{1}{75}\)
\(\dfrac{1}{2}x\dfrac{2}{3}x\dfrac{3}{4}x\dfrac{4}{5}x\dfrac{5}{6}x\dfrac{6}{7}...x\dfrac{98}{99}x\dfrac{99}{100}\\ =\dfrac{1x2x3x4x5x6x...x98x99}{2x3x4x5x6x7x...x99x100}\\ =\dfrac{1}{100}\)
