Ta có : \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)......\left(1-\frac{1}{2016}\right)\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{2015}{2016}.\frac{2016}{2017}\)
\(=\frac{1.2.3.....2016}{2.3.4.....2017}\)
\(=\frac{1}{2017}\)