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Question-74716




Question Number 74716 by chess1 last updated on 29/Nov/19
Answered by Tanmay chaudhury last updated on 29/Nov/19
x(1+(1/3))×x(1+(1/3^2 ))×...x(1+(1/3^(25) ))=1  x^(25) ×A=1  x=((1/A))^(1/(25)) when A=(1+(1/3))(1+(1/3^2 ))...(1+(1/3^(25) ))
$${x}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}\right)×{x}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)×…{x}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{25}} }\right)=\mathrm{1} \\ $$$${x}^{\mathrm{25}} ×{A}=\mathrm{1} \\ $$$${x}=\left(\frac{\mathrm{1}}{{A}}\right)^{\frac{\mathrm{1}}{\mathrm{25}}} {when}\:{A}=\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)…\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{25}} }\right) \\ $$

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