Question

[luong thi lai]

B=(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/2016)*(1-1/2017)

tính giá trị biểu thức

Answer 1

[Thúy Ngân]

\(B=\)\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)..\left(1-\frac{1}{2016}\right)\left(1-\frac{1}{2017}\right)\)

\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2015}{2016}.\frac{2016}{2017}\)

\(\Rightarrow B=\frac{1}{2017}\)

Answer 2

[Nguyễn Hưng Phát]

Ta có:\(B=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times............\times\left(1-\frac{1}{2017}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times............\times\frac{2016}{2017}\)

\(=\frac{1\times2\times..........\times2016}{2\times3\times...........\times2017}=\frac{1}{2017}\)