Giải thích các bước giải:
Ta có:
$C=\dfrac{1}{1!}+\dfrac{1}{2!}+\dfrac{1}{3!}+...+\dfrac{1}{2019!}$
$\to C=1+\dfrac{1}{1.2}+\dfrac{1}{1.2.3}+...+\dfrac{1}{1.2.3..2019}$
$\to C<1+\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2018.2019}$
$\to C<1+\dfrac{2-1}{1.2}+\dfrac{3-2}{2.3}+...+\dfrac{2019-2018}{2018.2019}$
$\to C<1+1-\dfrac12+\dfrac12-\dfrac12+...+\dfrac1{2018}-\dfrac1{2019}$
$\to C<2-\dfrac1{2019}$
$\to C<2-\dfrac14$
$\to C<\dfrac74$