Question

\(A=\)\(\left(1-\frac{1}{2018}\right)\)\(\left(1-\frac{2}{2018}\right)\)\(\left(1-\frac{3}{2018}\right)\)\(...\)\(\left(1-\frac{2020}{2018}\right)\)

Answer 1

\(A=\left(1-\frac{1}{2018}\right)\left(1-\frac{2}{2018}\right)\left(1-\frac{3}{2018}\right)...\left(1-\frac{2020}{2018}\right).\)

   \(=\frac{2017}{2018}\cdot\frac{2016}{2018}\cdot\frac{2015}{2018}\cdot...\cdot\left(1-\frac{2018}{2018}\right)\cdot...\cdot\frac{-2}{2018}\)

   \(=\frac{2017}{2018}\cdot\frac{2016}{2018}\cdot\frac{2015}{2018}\cdot...\cdot0\cdot...\cdot\frac{-2}{2018}\)

   \(=0\)