Đáp án:
Giải thích các bước giải:
1)S=2+2²+2³+2^4+...+2^100
⇔2S=2²+2³+2^4+...+2^100+2^101
⇔2S-S= (2²+2³+2^4+...+2^100+2^101)-(2+2²+2³+2^4+...+2^100)
⇔S=2^101 - 2
Vậy S=2^101-2
2)S=2+2³+2^5+...+2^99
⇔2².S=2^3+2^5+2^7+..+2^101
⇔4.S-S=(2^3+2^5+2^7+..+2^101)-(2+2^3+2^5+..+2^99)
⇔3S=2^101 - 2
⇔S=(2^101 - 2):3
Vậy S=(2^101-2):3
3)S=3+3^3+3^4+...+3^50
3S=S=3²+3^4+3^5+...+3^51
3S-S=(3²+3^4+3^5+...+3^51) - (3+3^3+3^4+...+3^50)
2S=3²+ 3^51 - 3 - 3³
S=3^51
Vậy S=3^51