\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{2015}\right)\times\left(1-\frac{1}{2016}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{2014}{2015}\times\frac{2015}{2016}\)
\(=\frac{1}{2016}\)
\(=\frac{1}{2}.\frac{2}{3}...\frac{2015}{2016}=\frac{1.2....2015}{2.3....2016}=\frac{1}{2016}\)
(1 - 1/2) . (1 - 1/3) . .... (1 - 1/2015) . (1- 2016)
= 1/2 . 2/3 .....2014/2015. 2015/2016
= 1.2.....2014.2015/2.3....2015.2016
= 1/2016
\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2014}{2015}.\frac{2015}{2016}=\frac{2.3.4...2015}{\left(2.3.4...2015\right).2016}=\frac{1}{2016}\)
