Đặt `A= 1/3 - 1/3^2 + 1/3^3 -...- 1/3^100`
`1/3 A= 1/3 ( 1/3 - 1/3^2 + 1/3^3-...- 1/3^100)`
`1/3 A= 1/3^2 - 1/3^3 + 1/3^4-...-1/3^101`
`A+ 1/3 A= 1/3 - 1/3^2 + 1/3^3 -...-1/3^100 + 1/3^2 - 1/3^3 + 1/3^4 -...-1/3^101`
`4/3 A = 1/3 - 1/3^101`
`A= (1/3 - 1/3^101): 4/3`
`A= (1/3 - 1/3^101) . 3/4`
`A= 1/4 - 1/(3^100 .4)`
Vậy `A= 1/4 - 1/(3^100 .4)`