1+\frac {x}{1!} + \frac {x^2}{2!}\lim_{n\rightarrow \infty}\left(1-\frac 1 n\right)+\frac {x^3}{3!}\lim_{n\rightarrow \infty}\left[\left(1-\frac 1 n\right)\left(1-\frac 2 n\right)\right]+ ...\\ 
+\lim_{n\rightarrow \infty}\left(\frac {x^k}{k!}\right)\lim_{n\rightarrow \infty}\left[\left(1-\frac 1 n\right)\left(1-\frac 2 n\right) ... \left(1-\frac {k-2} n\right)\left(1-\frac {k-1} n\right)\right]+ ...