2S = 2 + 2^2 + 2^3 + 2^4 + 2^5 + ... + 2^101
2S - S = 2 + 2^2 + 2^3 + 2^4 + 2^5 + ... + 2^101 - 1 - 2 - 2^2 - 2^3 - 2^4 -... - 2^100
S = 2^101 - 1
Bài 2.
6S = 6^2 + 6^3 + 6^4 + 6^5 + ... + 6^100
6S - S =  6^2 + 6^3 + 6^4 + 6^5 + ... + 6^100 - 6 - 6^2 - 6^3 - 6^4 - ... - 6^99
5S = 6^100 - 6
S = 6^100 - 6 / 5

B1: S = 1 + 2 + 2^2 + 2^3 +...... + 2^100
2S = 2 + 2^2 + 2^3 + 2^4 + ..... + 2^101
=> S = 2S  -S = (2 + 2^2 + 2^3 + 2^4 + ..... + 2^101) - (1 + 2 + 2^2 + 2^3 +...... + 2^100) = 2^101 - 1
B2: S = 6 + 6^2 +........ + 6^99
=> 6S = 6^2 + 6^3 + ..... + 6^100
=> 5S = 6S - S  = 6^100 - 6 => S = (6^100 - 6)/5

S=1+2+2^2+2^3+...+2^100
2S=2+2^2+2^3+...+2^101
2S-S=(2+2^2+2^3+...+2^101)-(1+2+2^2+2^3+...+2^100)
S=2^101-1
HT

Bài 1:
   S=1+2+2^2+2^3+2^4+...+2^100
2S=2+2^2+2^3+2^4+2^5+...+2^101
2S-S= (2+2^2+2^3+2^4+2^5+...+2^101)-(1+2+2^2+2^3+2^4+...+2^100)
2S-S= 2+2^2+2^3+2^4+2^5+...+2^101-1-2-2^2-2^3-2^4-...-2^100
   S=2^101-1
Bài 2:
S= 6+6^2+6^3+6^4+...+6^99
6S= 6^2+6^3+6^4+6^5+...+6^100
6S-S= ( 6^2+6^3+6^4+6^5+...+6^100)-(6+6^2+6^3+6^4+...+6^99)
6S-S= 6^2+6^3+6^4+6^5+...+6^100-6-6^2-6^3-6^4-...-6^99
5S= 6^100-6
S= (6^100-6)/5