Question

(1-\(\frac{1}{2}\)) x (1-\(\frac{1}{3}\))...(1-\(\frac{1}{2015}\)) x (1-\(\frac{1}{2016}\))

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Answer 1

\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{2015}\right)\times\left(1-\frac{1}{2016}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{2014}{2015}\times\frac{2015}{2016}\)

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

Answer 2

\(=\frac{1}{2}.\frac{2}{3}...\frac{2015}{2016}=\frac{1.2....2015}{2.3....2016}=\frac{1}{2016}\)

Answer 3

(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

 

Answer 4

\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2014}{2015}.\frac{2015}{2016}=\frac{2.3.4...2015}{\left(2.3.4...2015\right).2016}=\frac{1}{2016}\)