Question

(1-1/2)×(1-1/3)×(1-1/4)×...×(1-1/18)×(1-1/19)×(1-1/20)

Answer 1

\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{18}\right)\times\left(1-\frac{1}{19}\right)\times\left(1-\frac{1}{20}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{17}{18}\times\frac{18}{19}\times\frac{19}{20}\)

\(=\frac{1\times2\times3\times...\times17\times18\times19}{2\times3\times4\times...\times18\times19\times20}\)

\(=\frac{1}{20}\)