Question

Rut gon

A=(1-1/2).(1-1/3)...............(1-1/2017)

Answer 1

\(A=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)............\left(1-\dfrac{1}{2017}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\)..........\(.\dfrac{2016}{2017}\)

\(=\dfrac{1}{2017}\)

Answer 2

\(A=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{2017}\right)\\ =\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{2016}{2017}\\ =\dfrac{1\cdot2\cdot...\cdot2016}{2\cdot3\cdot...\cdot2017}\\ =\dfrac{1}{2017}\)