A=1.2.3.....99.100.(1+1/2+1/3+...+1/99+1/100)
=1.2.3.....99.100.[(1+1/100)+(1/2+1/99)+(1/3+1/98)+...+(1/50+1/51)]
=1.2.3.....99.100.(101/100+101/2.99+101/3.98+...+101/50.51)
=1.2.3.....99.100.101.(1/100+1/2.99+...+1/50.51)
Vì 101:101⇒A:101(đpcm)
Vậy số tự nhiên A chia hết cho 101