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Question Number 106644 by ZiYangLee last updated on 06/Aug/20

$$\mathrm{Let}\mathrm{P}\left(\mathrm{x}\right)\mathrm{be}\mathrm{a}\mathrm{polynomial}\mathrm{of}\mathrm{degree}\mathrm{n}$$$$\mathrm{with}\mathrm{real}\mathrm{coefficients}.$$$$\mathrm{Prove}\mathrm{that}\underset{\mathrm{k}=0}{\sum ^{\mathrm{n}}}\frac{{\mathrm{P}}^{\left(\mathrm{k}\right)}\left(0\right)}{(\mathrm{k}+1)!}=\underset{\mathrm{k}=0}{\sum ^{\mathrm{n}}}\frac{{(-1)}^{\mathrm{k}}{\mathrm{P}}^{\left(\mathrm{k}\right)}\left(1\right)}{(\mathrm{k}+1)!}$$$$$$

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