prove that all the roots of $\sum_{k=0}^{n}\frac{z^{k}}{k!}$ are in $\{z:\frac{n}{e}<|z|<2n\}$. I thought about using Rouché's theorem but there is no function which I can compare to. Does anyone have an idea?
2026-03-25 10:58:56.1774436336
prove that all the roots of $\sum_{k=0}^{n}\frac{z^{k}}{k!}$ are in $\{z:\frac{n}{e}<|z|<2n\}$
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