Giải thích các bước giải:
Đặt `A=1/2^2+1/2^3+1/2^4+...+1/2^100`
`=>2A=1/2+1/2^2+1/2^3+...+1/2^99`
`=>2A-A=(1/2+1/2^2+1/2^3+...+1/2^99)-(1/2^2+1/2^3+1/2^4+...+1/2^100)`
`=>A=1/2-1/2^100`
Mà `1/2^100>0=>-1/2^100<0=>1/2-1/2^100<1/2` hay `A<1/2`.
Vậy `1/2^2+1/2^3+1/2^4+...+1/2^100<1/2`.