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