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Question Number 116253 by I want to learn more last updated on 02/Oct/20

$$\left(1\right)\mathrm{Show}\mathrm{that}\underset{\mathrm{i}=0}{\sum ^{\mathrm{n}}}{\mathrm{L}}_{\mathrm{i}}\left(\mathrm{x}\right)=1$$$$\left(2\right)\mathrm{Show}\mathrm{that}\underset{\mathrm{i}=0}{\sum ^{\mathrm{n}}}{\mathrm{L}}_{\mathrm{i}}\left(\mathrm{x}\right).{\mathrm{x}}_{\mathrm{i}}^{\mathrm{k}}={\mathrm{x}}^{\mathrm{k}},\mathrm{k}⩽\mathrm{n}$$

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