Giải thích các bước giải:
c.Ta có :
$A=\dfrac{1}{2!}+\dfrac{2}{3!}+..+\dfrac{2019}{2020!}$
$\to A=\dfrac{2-1}{2!}+\dfrac{3-1}{3!}+..+\dfrac{2020-1}{2020!}$
$\to A=\dfrac{1}{1!}-\dfrac{1}{2!}+\dfrac{1}{2!}-\dfrac{1}{3!}+..+\dfrac{1}{2019!}-\dfrac{1}{2020!}$
$\to A=1-\dfrac{1}{2020!}<1$
Lại có :
$B=\dfrac{2018.2019-10}{2018.2018+2008}$
$\to B=\dfrac{2018.2019-10}{2018.2018+2018-10}$
$\to B=\dfrac{2018.2019-10}{2018.(2018+1)-10}$
$\to B=\dfrac{2018.2019-10}{2018.2019-10}=1$
$\to A<B$
