Question

[Jery Cheyry Gaming]

Tính : A = ( 1 - 1/2 ) *( 1 - 1/3 ) *( 1 - 1/4 ) *( 1 - 1/5 ) ..... ( 1 - 1/2016 ) *( 1 - 1/2017 )

Answer 1

[Phan Văn Hiếu]

\(A=\left(1-\frac{1}{2}\right).\left(1-\frac{2}{3}\right)...\left(1-\frac{1}{2017}\right)\)

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

\(A=\frac{1.2.3...2016}{2.3.4...2017}=\frac{1}{2017}\)

Answer 2

[Lucy Heartfilia]

\(A=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot\left(1-\frac{1}{5}\right)\cdot...\cdot\left(1-\frac{1}{2016}\right)\cdot\left(1-\frac{1}{2017}\right)\)

\(A=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot...\cdot\frac{2015}{2016}\cdot\frac{2016}{2017}\)

\(A=\frac{1\cdot2\cdot3\cdot4\cdot....\cdot2015\cdot2016}{2\cdot3\cdot4\cdot5\cdot....\cdot2016\cdot2017}\)

\(A=\frac{1}{2017}\)