Question

1+4+4^2+4^3+...+4^27 comparat cu 2^56-1

Answer 1

1+4+4^2+4^3+...+4^27 comparat cu 2^56-1

1+a+a^2+a^3+...+a^n=[a^(n+1)-1]/(a-1)

1+4+4^2+4^3+...+4^27=(4^28 -1)/3

2^56-1=2^(2•28)-1=4^28-1

(4^28 -1)/3 < 4^28 -1

1+4+4^2+4^3+...+4^27 <  2^56-1