Question

tính giá trị biểu thức:B=(1-1/2).(1-1/3).(1-1/4)...(1-1/2021).(1-1/2022) nhờ mọi người giải với ạ

 

Answer 1

\(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{2020}{2021}\cdot\dfrac{2021}{2022}=\dfrac{1}{2022}\)

Answer 2

\(B=\left(1-\dfrac{1}{2}\right)\cdot\left(1-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}\right)\cdot\cdot\cdot\left(1-\dfrac{1}{2021}\right)\cdot\left(1-\dfrac{1}{2022}\right)\)

\(B=\left(\dfrac{2}{2}-\dfrac{1}{2}\right)\cdot\left(\dfrac{3}{3}-\dfrac{1}{3}\right)\cdot\left(\dfrac{4}{4}-\dfrac{1}{4}\right)\cdot\cdot\cdot\left(\dfrac{2021}{2021}-\dfrac{1}{2021}\right)\cdot\left(\dfrac{2022}{2022}-\dfrac{1}{2022}\right)\)

\(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\cdot\cdot\dfrac{2020}{2021}\cdot\dfrac{2021}{2022}\)

\(B=\dfrac{1\cdot2\cdot3\cdot\cdot\cdot2020\cdot2021}{2\cdot3\cdot4\cdot\cdot\cdot2021\cdot2022}\)

\(B=\dfrac{1}{2022}\)

Answer 3

B=(1-1/2).(1-1/3).(1-1/4)...(1-1/2021).(1-1/2022)

B = 1/2 . 2/3 . 3/4 ... 2020/2021 . 2021/2022

B = \(\dfrac{1.2.3.....2020.2021}{2.3.4......2021.2022}\)

\(B=\dfrac{1}{2022}\)