\(B=\)\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)..\left(1-\frac{1}{2016}\right)\left(1-\frac{1}{2017}\right)\)
\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2015}{2016}.\frac{2016}{2017}\)
\(\Rightarrow B=\frac{1}{2017}\)
Ta có:\(B=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times............\times\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times............\times\frac{2016}{2017}\)
\(=\frac{1\times2\times..........\times2016}{2\times3\times...........\times2017}=\frac{1}{2017}\)
\(B=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot....\cdot\left(1-\frac{1}{2016}\right)\cdot\left(1-\frac{1}{2017}\right)\)
\(B=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot....\cdot\frac{2015}{2016}\cdot\frac{2016}{2017}\)
\(\Rightarrow B=\frac{1}{2017}\)
B=(1-1/2).(1-1/3).(1-1/4)....(1-1/2016).(1-1/2017)
B=1/2.2/3.3/4....2015/2016.2016/2017
B=1/2017