Question

\(A=\left(1-\dfrac{1}{2}\right)\cdot1-\dfrac{1}{3}\cdot......\cdot\left(1-\dfrac{1}{2016}\right)\cdot\left(1-\dfrac{1}{2017}\right)\)

Answer 1

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

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

Answer 2

Giải:

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

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

\(\Leftrightarrow A=\dfrac{1.2...201.2016}{2.3...2016.2017}\)

\(\Leftrightarrow A=\dfrac{1.2.3...2015.2016}{2017.2.3...2015.2016.}\)

Rút gọ cả tử và mẫu với 2.3...2015.2016, ta được:

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

Vậy \(A=\dfrac{1}{2017}\).

Chúc bạn học tốt!

Answer 3

Giải:

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

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

Vậy, A= \(\dfrac{1}{2017}\)