How many ways can we calculate these limitations about factorial? $$1+a+\frac{a^2}{2!}+\frac{a^3}{3!}+...+\frac{a^n}{n!}\\ \frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-+...+\frac{(-1)^n}{n!}$$ I met this kind of limitations when I dealt with Poisson random variables and don't know how to solve them.
2026-04-04 02:12:01.1775268721
A Question Regarding Limitations
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The first converges to $e^a$ (it is the exponential series) and the latter is the special case where $a=-1$, so converges to $e^{-1}$.