Ta thấy

1.3.5.....19 = 1.2.3.4.5.6.....19.20/2.4.6.....20

= 1.2.3.4.5.6.....19.20/1.2.2.2.3.2.....10.2

= 1.2.3.4.5.6.....19.20/(1.2.3.....10).(2.2.2.....2) 

= (1.2.3.4.5.6.....10).(11.12.13.....19.10)/(1.2.3.....10).(2.2.2.....2)

= 11.12.13.....19.20/2.2.2.....2

= 11/2 . 12/2 . 13/2 . ... . 19/2 . 20/2

=> Đpcm

Ta có:

1.3.5...19 = 1.2.3.4.5.6...19.20/2.4.6...20

                 = 1.2.3.4.5.6...19.20/2^10.(1.2.3...10)

                 = 11.12.13....20/2^10

                 = 11/2 . 12/2 . 13/2 ... 20/2 ( đpcm)

Hình như thiếu đề hay sao ấy

\(1\cdot3\cdot5\cdot...\cdot19=\dfrac{1\cdot2\cdot3\cdot4\cdot...\cdot17\cdot18\cdot19\cdot20}{2\cdot4\cdot6\cdot8\cdot...\cdot20}\)

\(=\dfrac{1\cdot2\cdot3\cdot4\cdot...\cdot17\cdot18\cdot19\cdot20}{1\cdot2\cdot2\cdot2\cdot3\cdot2\cdot4\cdot2\cdot...\cdot10\cdot2}\)

\(=\dfrac{11}{2}\cdot\dfrac{12}{2}\cdot...\cdot\dfrac{18}{2}\cdot\dfrac{19}{2}\)