Răspuns:
Explicație pas cu pas:
a)1+2+2^2+2^3 = 1+2+4+8 = 15
S= (1+2+2^2+2^3)+2^4(1+2+2^2+2^3)+
+ 2^8(1+2+2^2+2^3) +...+2^96(1+2+2^2+2^3)
S = (1+2+2^2+2^3)(1+2^4 + 2^8 + ...+2^96)
= 15(1+2^4 + 2^8 + ...+2^96) = multiplu de 15
b) S = prog geom. cu q = 2, si n = 99+1 = 100
S = 1*(2^100 - 1)/(2-1) = 2^100 - 1
10^30 are 30 de 0 +1 = 31 cifre
10^30 < 2^100 pt. ca:
(10^3)^10 < (2^10)^10
10^3 < 2^10
1000 < 1024
S se termina cu cel putin 30 cifre
