Question

1/5 + 1/10 + 1/20 + 1/40 +....+ 1/1280.

Answer 1

`A=1/5+1/10+1/20+1/40+....+1/1280`

`A=1/5(1+1/2+1/4+1/8+....+1/256)`

`2A=1/5(2+1+1/2+1/4+.....+1/128)`

`=>2A-A=A=1/5(2-1/256)`

`=>A=511/1280`

Answer 2

đặt `A = 1/5 + 1/10 + 1/20 + 1/40 + ... + 1/1280`

`=> A = 1/5(1 + 1/2 + 1/4 + 1/8 + ... + 1/256)`

`=> 2A = 1/5 . 2 (1 + 1/2 + 1/4 + 1/8 + .... + 1/256)`

`=> 2A = 1/5 . (2 + 1 + 1/2 + 1/4 + .... + 1/128)`

`-` 

A = 1/5(1 + 1/2 + 1/4 + 1/8 + ... + 1/256)`

`=> A = 1/5 . (2 - 1/256)`

`=> A = 1/5 . 511/256`

`=> A = 511/1280`

Vậy `A = 511/1280`