Question

(1-1/2)x(1-1/3)x(1-1/4)x...x(1-1/2015)x(1-1/2016)

Answer 1

(1-1/2)x(1-1/3)x(1-1/4) x ...x (1-1/2016)

= 1/2x2/3x3/4x.....x2015/2016

= \(\frac{1x2x3x...x2015}{2x3x4x...x2016}\)

= 1/2016

Answer 2

\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{2016}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times...\times\frac{2015}{2016}\)

\(=\frac{1}{2016}\)