Đặt:
`A = 1/2 + 1/4 + 1/8 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024`
`2 × A = 2 × (1/2 + 1/4 + 1/8 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024)`
`2 × A = 1 + 1/2 + 1/4 + 1/16 + 1/32 + ... + 1/512`
`2 × A - A = (1 + 1/2 + 1/4 + 1/16 + 1/32 + ... + 1/512) - (1/2 + 1/4 + 1/8 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024)`
`A = 1 + 1/2 + 1/4 + 1/16 + 1/32 + ... + 1/512 - 1/2 - 1/4 - 1/8 - .... - 1/512 - 1/1024`
`A = 1 - 1/1024`
`A = 1023/1024`