\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{2016}{2017}\)
\(=\frac{1\cdot2\cdot3\cdot4\cdot...\cdot2016}{2\cdot3\cdot4\cdot....\cdot2017}\)
\(=\frac{1}{2017}\)
Ta có:
\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.........\frac{2016}{2017}\)
\(=\frac{1.2.3......2016}{2.3.4......2017}\)
\(=\frac{1}{2017}\)
Vậy: \(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.........\frac{2016}{2017}\)\(=\frac{1}{2017}\)
Ta có:
\(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times.....\times\frac{2016}{2017}\)
\(\Rightarrow\frac{1\times2\times3\times.....\times2016}{2\times3\times4\times....\times2017}=\frac{1}{2017}\)
Vậy giá trị biểu thức là \(\frac{1}{2017}\)
=(1x2x3x...x2016)/((2x3x4x...x2017)=1/2017
