Question

Aflati x din: a) 1+2+ 2 la a doua+2 la a treia +...+ 2 la puterea X = 2 la putera 64 - 1
b) 99+2(1+2+3+...+x)=99 la a doua

Answer 1

Fie a=1+2+2^2+...+2^x, atunci 
     2a=2(1+2+2^2+...+2^x)=2+2^2+2^3+...+2^(x+1)
2a-a=2+2^2+2^3+...+2^(x+1)-1-2-2^2-2^3-...-2^x
a=2^(x+1) - 1
a=2^64 - 1
Din ultimele doua rezulta 2^(x+1)-1=2^64 -1
2^(x+1)=2^64
x+1=64
x=63