$(1+x)^n \ge \frac{n(n-1)}{2}x^2$ is there something wrong in my proof? This problem comes from my textbook, and I think it has mistake with equality sign, but if it doesn't, please, give me some hints. Here is the problem. It asks me to show inequality by using binomial theorem

And here is my steps

as  cannot be ZERO i think there shouldn't be equality sign. maybe x should have been choosen as -1  and n=1 for example? Thanks and sorry for bad english.

Your proof is correct, just observe that if $a>0$ is true then $a\geq0$ is true, in the latter you have $a=0$  $\color{red}{or}$ $a>0$.
