tính nhanh 1+1/1+2+1/1+2+3+1/1+2+3+4+.....1/1+2+3+...+2019

Question

uyenthu · Answer

Đ&aacute;p &aacute;n:    =71

huyenmi · Answer

Đặt:

`A = 1 + 1/(1 + 2) + 1/(1+2+3) + 1/(1 + 2 + 3 + 4) .+ … + 1/(1 + 2 + 3 + … + 2019)`

`A = 1 + (1/(1 + 2) + 1/(1+2+3) + 1/(1 + 2 + 3 + 4) .+ … + 1/(1 + 2 + 3 + … + 2019))`

Đặt:

`B = 1/(1 + 2) + 1/(1+2+3) + 1/(1 + 2 + 3 + 4) .+ … + 1/(1 + 2 + 3 + … + 2019)`

`B = 2/(2 . (1 + 2)) + 2/(2.(1 + 2 + 3)) + 2/(2 . (1 + 2 + 3 + 4)) + … + 2/(2 . (1 + 2 + 3 + … + 2019))`

`B = 2/(2 . 3) + 2/(2.6) + 2/(2 . 10) + … + 2/(2 . 2039190)`

`B = 2 . (1/(2.3) + 1/(3.4) + 1/(4.5) + … + 1/(2019 . 2020)`

`B = 2 . (1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/2019 – 1/2020)`

`B = 2 . (1/2 – 1/2020)`

`B = 2 . 1009/2020`

`B = 2018/2020`

`=> A = 1 + 2018/2020`

`=> A = 2020/2020 + 2018/2020`

`=> A = 2019/1010`

tính nhanh 1+1/1+2+1/1+2+3+1/1+2+3+4+…..1/1+2+3+…+2019