Question Number 148284 by 0731619 last updated on 26/Jul/21
Answered by Olaf_Thorendsen last updated on 26/Jul/21
$$\mathrm{6}!!\:=\:\mathrm{6}×\mathrm{4}×\mathrm{2}\:=\:\mathrm{48} \\ $$$$\mathrm{8}!!!!!\:=\:\mathrm{8}×\mathrm{3}\:=\:\mathrm{24} \\ $$$$\mathrm{9}!!!!\:=\:\mathrm{9}×\mathrm{5}×\mathrm{1}\:=\:\mathrm{45} \\ $$$$!\mathrm{4}\:=\:\mathrm{4}!\left(\frac{\mathrm{1}}{\mathrm{0}!}−\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}\right)\:=\:\mathrm{9} \\ $$$$!\mathrm{5}\:=\:\mathrm{5}!\left(\frac{\mathrm{1}}{\mathrm{0}!}−\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}−+\frac{\mathrm{1}}{\mathrm{4}!}−\frac{\mathrm{1}}{\mathrm{5}!}\right)\:=\:\mathrm{44} \\ $$$${x}\:=\:!\mathrm{5}×\frac{\sqrt{!\mathrm{4}+\mathrm{8}!!!!!+\mathrm{6}!!−\mathrm{16}}}{\mathrm{9}!!!!} \\ $$$${x}\:=\:\mathrm{44}×\frac{\sqrt{\mathrm{9}+\mathrm{24}+\mathrm{48}−\mathrm{16}}}{\mathrm{45}}\:=\:\frac{\mathrm{44}}{\mathrm{9}}\sqrt{\frac{\mathrm{13}}{\mathrm{5}}} \\ $$
Commented by Sozan last updated on 26/Jul/21
$${msr}\:{olaf}\:{can}\:{you}\:{give}\:{me}\:{name}\:{book} \\ $$$${containd}\:{this}\:{factorial}\: \\ $$
Commented by Olaf_Thorendsen last updated on 26/Jul/21
$$\mathrm{Unfortunately}\:\mathrm{not}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{am}\:\mathrm{not}\:\mathrm{a}\:\mathrm{mathematician}. \\ $$$$\mathrm{I}\:\mathrm{use}\:\mathrm{my}\:\mathrm{phone},\:\mathrm{google}\:\mathrm{and}\:\mathrm{wikipedia}. \\ $$