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Question Number 148776 by liberty last updated on 31/Jul/21

Answered by mathmax by abdo last updated on 31/Jul/21

$$\mathrm{P}=\prod _{\mathrm{k}=2}^{2020}\frac{{\mathrm{k}}^2}{{\mathrm{k}}^2-1}=\prod _{\mathrm{k}=2}^{2020}\frac{\mathrm{k}}{\mathrm{k}-1}\times \frac{\mathrm{k}}{\mathrm{k}+1}$$$$=\prod _{\mathrm{k}=2}^{2020}\frac{\mathrm{k}}{\mathrm{k}-1}\times \prod _{\mathrm{k}=2}^{2020}\frac{\mathrm{k}}{\mathrm{k}+1}$$$$=\frac{2}{1}\times \frac{3}{2}\times \frac{4}{3}.....\frac{2019}{2018}\times \frac{2020}{2019}\times \frac{2}{3}.\frac{3}{4}.\frac{4}{5}.....\frac{2019}{2020}.\frac{2020}{2021}$$$$=2020\times \frac{2}{2021}=\frac{4040}{2021}$$

Commented by liberty last updated on 31/Jul/21

$$\mathrm{nice}\mathrm{sir}$$

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