Question

tính

\(A=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right).....\left(\dfrac{1}{2021}\right)\)

Answer 1

`A=\(\frac{1}{2}-1)(\dfrac{1}{3}-1).....(\frac{1}{2021}-1)`

`=\frac{-1}{2}.\frac{-2}{3}.....\frac{-2020}{2021}`
`=(-1xx(-2)xx...xx(-2020))/(2xx3xx....xx2021)`
`=(1xx2xx..xx2020)/(2xx3xx...xx2021)`(do `1->2020` có 2020 số)

`=\frac{1}{2021}`

Answer 2

Cái cuối có -1 ko

Answer 3

\(A=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right).....\left(\dfrac{1}{2021}-1\right)\)

\(=\dfrac{-1}{2}.\dfrac{-2}{3}.....\dfrac{-2020}{2021}\)

\(=1.\dfrac{1}{2021}=\dfrac{1}{2021}\)

Answer 4

Giải: 

\(A=\left(\dfrac{1}{2}-1\right).\left(\dfrac{1}{3}-1\right).....\left(\dfrac{1}{2021}-1\right)\) 

\(A=\dfrac{-1}{2}.\dfrac{-2}{3}.....\dfrac{-2020}{2021}\) 

\(A=\dfrac{-1.-2.....-2020}{2.3.....2021}\) 

\(A=\dfrac{1}{2021}\) 

Chúc bạn học tốt!