Question

Tính

(1-\(\dfrac{1}{2}\))(1-\(\dfrac{1}{3}\))(1-\(\dfrac{1}{4}\)).....(1-\(\dfrac{1}{2017}\))

Answer 1

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{5}\right)...\left(1-\dfrac{1}{2017}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}....\dfrac{2016}{2017}\)

\(=\dfrac{1}{2017}\)

Answer 2

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right).....\left(1-\dfrac{1}{2017}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.....\dfrac{2016}{2017}\)

\(=\dfrac{1.2.3.....2016}{2.3.4.....2017}\)

\(=\dfrac{1}{2017}\)

Answer 3

Giải:

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2017}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{2016}{2017}\)

\(=\dfrac{1}{2017}\)

Vậy giá trị của biểu thức trên là \(\dfrac{1}{2017}\).

Chúc bạn học tốt!

Answer 4

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)....\left(1-\dfrac{1}{2017}\right)\)

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

= \(\dfrac{1.2....2016}{2.3....2017}\)

= \(\dfrac{1}{2017}\)