Đặt `A = 1/2 + 1/4 + 1/8 + 1/16 +...+ 1/1024 +1/2048`
`A = 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +...+ 1/2^10 + 1/2^11`
`2A = 2( 1/2 + 1/2^2 + 1/2^3 + 1/2^4 +...+ 1/2^10 + 1/2^11)`
`2A = 1 + 1/2 + 1/2^2 + 1/2^3+...+ 1/2^10`
`2A -A = 1 + 1/2 + 1/2^2 + 1/2^3+...+ 1/2^10- 1/2 - 1/2^2 - 1/2^3-....- 1/2^11)`
`A = 1- 1/2^11`
Vậy `A = 1- 1/2^11`