Question

(1-1/2)(1-1/3)(1-1/4)...(1-1/2020)

Answer 1

Answer 2

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2020}\right)=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{2019}{2020}=\dfrac{1}{2020}\)

Answer 3

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{2020}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{2019}{2020}\)

\(=\dfrac{1}{2020}\)