Đáp án:
`S=2^101-1`
Giải thích các bước giải:
`S=1+2+2^2+...+2^99+2^100`
`⇒2S=2.(1+2+2^2+...+2^99+2^100)`
`⇒2S=2+2^2+...+2^100+2^101`
`⇒2S-S=(2+2^2+...+2^100+2^101)-(1+2+2^2+...+2^99+2^100)`
`⇒S=2+2^2+...+2^100+2^101-1-2-2^2-...-2^99-2^100`
`⇒S=2^101-1`
Vậy `S=2^101-1`