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**Warning:Danger Ahead**

hello all

over the last few days Iv been working on this question, but i am seriously left speachless, this will most likely be the hardest question I have ever attempted if anybody is up for a challenge be prepared... alright here we go

we have [tex]\forall n\in\aleph[/tex]

[tex] F(n)= 2n+\frac{2}{3}-e^n\sum_{k=0}^{n-1}\frac{(k-n)^k e^{-k}}{k!}[/tex]

Prove

[tex]\lim_{n\rightarrow\infty} F(n)=0[/tex]