`S= 1/2^2 + 1/2^3 + 1/2^4 +....+ 1/2^100`
`1/2 S = 1/2( 1/2^2 + 1/2^3 + 1/2^4 +...+ 1/2^100)`
`1/2 S= 1/2^3 + 1/2^4 + 1/2^5 +...+ 1/2^101`
`S- 1/2S = 1/2^2+ 1/2^3 + 1/2^4 +...+ 1/2^100 - 1/2^3 - 1/2^4- 1/2^5 -...- 1/2^101`
`1/2 S= 1/2^2 - 1/2^101`
`S= (1/2^2 - 1/2^101) : 1/2`
`S= (1/2^2 - 1/2^101) . 2`
`S= 1/2 - 1/2^100`
Vì `1/2< 1`
`=> 1/2 - 1/2^100 < 1`
Vậy `S < 1`
