Prove a Little o inequality

Question

I've managed to reduce a proof to the following: I now need to show that $e$$k \choose 2$$(1+f(k))^k<1$ for some $f(k)=o(1)$. I'm thinking the general inequalities $1/e \leq (1-1/(n+1))^n$, or $1/e \geq (1-1/n)^n$ could be useful somehow (e.g. if that $k \choose 2$ factor wasn't there I could just use $f(k)=-1/k$.). But in this case I am not sure what $f(k)$ should be.