Question Number 63561 by aliesam last updated on 05/Jul/19
Answered by MJS last updated on 05/Jul/19
![=Π_(k=1) ^n (2k−1)×Π_(k=1) ^n 2k= =[1×3×5×...×(2n−1)]×[2×4×6×...×2n]= =1×2×3×4×...×(2n−1)(2n)= =(2n)!](Q63562.png)
$$=\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{2}{k}−\mathrm{1}\right)×\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\mathrm{2}{k}= \\ $$$$=\left[\mathrm{1}×\mathrm{3}×\mathrm{5}×...×\left(\mathrm{2}{n}−\mathrm{1}\right)\right]×\left[\mathrm{2}×\mathrm{4}×\mathrm{6}×...×\mathrm{2}{n}\right]= \\ $$$$=\mathrm{1}×\mathrm{2}×\mathrm{3}×\mathrm{4}×...×\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}\right)= \\ $$$$=\left(\mathrm{2}{n}\right)! \\ $$
Commented by aliesam last updated on 05/Jul/19
$${god}\:{bless}\:{you}\:{sir} \\ $$