Răspuns:
Explicație pas cu pas:
a= 1 + 2 +2^2 +2^3 + ... + 2^100 + 2^101
2a = 2 +2^2 +2^3 + 2^4 +... + 2^101 + 2^102
2a - a = 2 +2^2 +2^3 + 2^4 +... + 2^101 + 2^102 - 1 - 2 - 2^2 - 2^3 - ... - 2^100 - 2^101 = 2^102 - 1
__________
S = 1 + 4 + 4^2 + ... + 4^50
4S = 4 + 4^2 + 4^3 + ... + 4^51
4S - S = 4 + 4^2 + 4^3 + ... + 4^51 - 1 - 4 - 4^2 - ... - 4^50
3S = 4^51 - 1
S = (4^51 - 1)/3
______________
b = 3*(4^51 - 1)/3 = 4^51 - 1 = (2^2)^51 - 1 = 2^102 - 1 = a
