Toán 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100 30/06/2021 By Skylar 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100
Đặt `A = 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100` `=> 3A =1 + 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^99` `=> 3A – A = (1 + 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^99) – (1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100)` `=> 2A = 1 – 1/3^100` `=> A = (1- 1/3^100)/2` Trả lời
Đáp án + Giải thích các bước giải: Đặt `A=1/3+1/3^2+1/3^3+…+1/3^100` `=>3A=1+1/3+1/3^2+…+1/3^99` `=>3A-A=(1+1/3+1/3^2+…+1/3^99)-(1/3+1/3^2+1/3^3+…+1/3^100)` `=>2A=1-1/3^100` `=>A=(1-1/3^100)/2` Trả lời
Đặt `A = 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100`
`=> 3A =1 + 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^99`
`=> 3A – A = (1 + 1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^99) – (1/3+1/3^2+1/3^3+1/3^4+…+1/3^99+1/3^100)`
`=> 2A = 1 – 1/3^100`
`=> A = (1- 1/3^100)/2`
Đáp án + Giải thích các bước giải:
Đặt `A=1/3+1/3^2+1/3^3+…+1/3^100`
`=>3A=1+1/3+1/3^2+…+1/3^99`
`=>3A-A=(1+1/3+1/3^2+…+1/3^99)-(1/3+1/3^2+1/3^3+…+1/3^100)`
`=>2A=1-1/3^100`
`=>A=(1-1/3^100)/2`