Giải thích các bước giải:
Ta có :
$M=(1+\dfrac12+\dfrac13+..+\dfrac1{98})\cdot 2\cdot 3\cdot 4....\cdot 98$
$\to M=((1+\dfrac1{98})+(\dfrac12+\dfrac1{97})+(\dfrac13+\dfrac1{96})+..+(\dfrac1{49}+\dfrac1{50}))\cdot 2\cdot 3\cdot 4....\cdot 98$
$\to M=(\dfrac{1+98}{1\cdot 98}+\dfrac{2+97}{2\cdot 97}+\dfrac{3+96}{3\cdot 96}+..+\dfrac{49+50}{49\cdot 50})\cdot 2\cdot 3\cdot 4....\cdot 98$
$\to M=(\dfrac{99}{1\cdot 98}+\dfrac{99}{2\cdot 97}+\dfrac{99}{3\cdot 96}+..+\dfrac{99}{49\cdot 50})\cdot 2\cdot 3\cdot 4....\cdot 98$
$\to M=99(\dfrac{1}{1\cdot 98}+\dfrac{1}{2\cdot 97}+\dfrac{1}{3\cdot 96}+..+\dfrac{1}{49\cdot 50})\cdot 2\cdot 3\cdot 4....\cdot 98$
Ta thấy :
$(\dfrac{1}{1\cdot 98}+\dfrac{1}{2\cdot 97}+\dfrac{1}{3\cdot 96}+..+\dfrac{1}{49\cdot 50})\cdot 2\cdot 3\cdot 4....\cdot 98\in Z$
$\to M\quad\vdots\quad 99$
