Prove that the limiting distribution of $nF[X_{(2)}]$ Gamma(2,1).

Question

I am working on a problem stated in the title.

So far I know that the cdf for $X_{(2)}$ is $$F_{X_{(2)}}(x)=1-[1-F(x)]^n-nF(x)[1-F(x)]^{n-1}$$ and that I am to prove that $$nF(X_{(2)}) \rightarrow 1-e^{-x}-xe^{-x}$$

I do not know what to do when I take the limit as $n \rightarrow \infty$ ...

I appreciate your help.