Question

aratati ca x este patrat perfect din relatia 2^1+2^2+2^3+..+2^101

Answer 1

$x=2^1+2^2+2^3+..+2^{101}|\cdot 2\\ \\2x=2^2+2^3+..2^{101}+2^{102}|+2\\2x+2=x+2^{102}\\x=2^{102}-2\\u(2^{102})=4\\u(x)=2=>x\ nu \ este \ patrat\ perfect.$