Question

daca A= 1 +2+ 2 la puterea doua + ... + 2 la puterea 11, demonstrati ca ca 1 +A este cub perfect

Answer 1

[tex]A=1+2+2^2+....+2^{11}\\ -2A=-2-2^2-2^3-...-2^{12}\\ .................................................\\ -A=1-2^{12}\\ A=2^{12}-1 A+1=2^{12}\\ A+1=(2^4)^3[/tex]