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\(1\cdot3\cdot5\cdot...\cdot19=\dfrac{1\cdot2\cdot3\cdot4\cdot...\cdot17\cdot18\cdot19\cdot20}{2\cdot4\cdot6\cdot8\cdot...\cdot20}\)
\(=\dfrac{1\cdot2\cdot3\cdot4\cdot...\cdot17\cdot18\cdot19\cdot20}{1\cdot2\cdot2\cdot2\cdot3\cdot2\cdot4\cdot2\cdot...\cdot10\cdot2}\)
\(=\dfrac{11}{2}\cdot\dfrac{12}{2}\cdot...\cdot\dfrac{18}{2}\cdot\dfrac{19}{2}\)
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. (2.4.6...20/2.4.6....20)=1.2.3....19.20/(1.2.3....10)(2.2.2.2.2.2.2.2.2.2)=11/2 .12/2 ......20/2
10 chữ số 2
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)
