Đáp án:

Giải thích các bước giải:

`a) 2^1 + 2^2 + 2^3 + 2^4 + .. + 2^99 + 2^100`

`= (2+2^2) + (2^3+2^4) +...+2^99+2^100`

`= 2(1 + 2) + 2^3(1 + 2) + .... + 2^99(1 + 2)`

`= 2 . 3 + 2^3 . 3 + ... +2^99 . 3`

`= 3 . (2 + 2^3 + ... + 2^99)2` chia hết cho `3`

`b) 2^1 + 2^2 + 2^3 + 2^4 + ... + 2^99 + 2^100`

`= 2 + (2^2+2^3+2^4) +(2^5+2^6+2^7) +  .... + (2^98+2^99+2^100)`

`= 2 + 2^2(1+2+2^2) + 2^5(1+2+2^2) + ... + 2^98(1+2+2^2)`

`= 2 + 2^2 . 7 + 2^5 . 7 + ... + 2^98 . 7`

`= 2 + 7(2^2+2^5+...+2^98)` chia `7` dư `2`