Giải thích các bước giải:
Ta có:
$M=\dfrac{1}{1!}+\dfrac1{2!}+\dfrac{1}{3!}+...+\dfrac{1}{100!}$
$\to M=1+\dfrac1{2!}+\dfrac{1}{3!}+...+\dfrac{1}{100!}$
$\to M<1+\dfrac1{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}$
$\to M<1+\dfrac{2-1}{1.2}+\dfrac{3-2}{2.3}+...+\dfrac{100-99}{99.100}$
$\to M<1+1-\dfrac12+\dfrac12-\dfrac13+...+\dfrac1{99}-\dfrac1{100}$
$\to M<2-\dfrac1{100}$
$\to M<2$
$\to -M>-2$
$\to 3!-M=6-M>6-2=4$
