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Cute solution.
[tex]\lim_{n\to+\infty}e^{-n}\sum_{i=n}^{+\infty}\frac{n^i}{i!}[/tex]
[tex]\lim_{n\to+\infty}e^{-n}\sum_{i=n}^{+\infty}\frac{n^i}{i!}[/tex]
that is the formula for e approximation. i did that in programming, but not approaching infinity, it should be real number.. i might be wrong.
First correction[tex]\lim_{n\to\infty}e^{-n}\sum_{i=n}^{\infty}\frac{n^i}{i!}[/tex]
[tex]\lim_{n\to\infty}e^{-n}(e^n - \sum_{i=0}^n \frac{x^n}{n!})[/tex]