Question

tinh :

A= ( 1-1/2) x ( 1-1/3) x ( 1-1/4) +.....+ ( 1-1/2017) x ( 1- 1/2018)

Answer 1

A = (1 - 1/2) x (1 - 1/3) x (1 - 1/4) + ... + (1 - 1/2017) x (1 - 1/2018)
<=> A = 1/2 x 2/3 x 3/4 x ... x 2016/2017 x 2017/2018
<=> A = \(\dfrac{1\times2\times3\times...\times2016\times2017}{2\times3\times4\times...\times2017\times2018}\)
<=> A = \(\dfrac{1}{2018}\)
@Nguyễn Linh Ly

Answer 2

\(A=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2017}\right)\left(1-\dfrac{1}{2018}\right)\)\(A=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{2016}{2017}.\dfrac{2017}{2018}\)

\(A=\dfrac{1.2.3....2016.2017}{2.3.4....2017.2018}\)

\(A=\dfrac{1}{2018}\)