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Question Number 163040 by qaz last updated on 03/Jan/22

$$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{\mathrm{n}!}{{\mathrm{n}}^{\mathrm{n}}}(\underset{\mathrm{k}=0}{\sum ^{\mathrm{n}}}\frac{{\mathrm{n}}^{\mathrm{k}}}{\mathrm{k}!}-\underset{\mathrm{k}=\mathrm{n}+1}{\sum ^{\mathrm{\infty }}}\frac{{\mathrm{n}}^{\mathrm{k}}}{\mathrm{k}!})=?$$

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