a= 1+ 2^{0} + 2^{1} + 2^{2} +.....+ 2^{999} [/tex] sa aratam ca e patrat perfect.

[tex]A=1+ \frac{2^{1000}-1}{2-1}=1+2^{1000}-1=2^{1000}=(2^{500})^2 -~patrat~perfect.[/tex]

[tex]Am~aplicat~formula:~1+a+a^2+...+a^n= \frac{a^{n+1}-1}{a-1}. [/tex]