Giải thích các bước giải:
Ta có:
$A=\dfrac{1}{2!}+\dfrac{1}{3!}+...+\dfrac{1}{n!}$
$\to A<\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{(n-1).n}$
$\to A<\dfrac{2-1}{1.2}+\dfrac{3-2}{2.3}+...+\dfrac{n-(n-1)}{(n-1).n}$
$\to A<\dfrac11-\dfrac12+\dfrac12-\dfrac13+...+\dfrac1{n-1}-\dfrac1n$
$\to A<1-\dfrac1n$
$\to A<1$