Question Number 98453 by rb222 last updated on 14/Jun/20
$$\frac{{m}}{\mathrm{1}×\mathrm{2}}×\frac{{m}}{\mathrm{2}×\mathrm{3}}×\frac{{m}}{\mathrm{3}×\mathrm{4}}×...×\frac{{m}}{\mathrm{99}×\mathrm{100}}=\mathrm{99} \\ $$$$ \\ $$$${m}? \\ $$
Commented by mr W last updated on 14/Jun/20
$$\frac{{m}^{\mathrm{99}} ×\mathrm{1}}{\left(\mathrm{1}×\mathrm{2}×\mathrm{3}×...×\mathrm{99}\right)×\left(\mathrm{1}×\mathrm{2}×\mathrm{3}×\mathrm{4}×...×\mathrm{100}\right)}=\mathrm{99} \\ $$$$\frac{{m}^{\mathrm{99}} }{\mathrm{99}!×\mathrm{100}!}=\mathrm{99} \\ $$$${m}^{\mathrm{99}} =\mathrm{99}×\mathrm{99}!×\mathrm{100}! \\ $$$$\Rightarrow{m}=\sqrt[{\mathrm{99}}]{\mathrm{99}×\mathrm{99}!×\mathrm{100}!}\approx\mathrm{1553}.\mathrm{349} \\ $$
Commented by rb222 last updated on 14/Jun/20
$${thanks}\:{sir} \\ $$