Giải thích các bước giải:
Ta có :
$A=\dfrac{102}{101!}-\dfrac{103}{102!}+\dfrac{104}{103!}-\dfrac{105}{104!}+..+\dfrac{2018}{2017!}-\dfrac{2019}{2018!}$
$\to A=\dfrac{101+1}{101!}-\dfrac{102+1}{102!}+\dfrac{103+1}{103!}-\dfrac{104+1}{104!}+..+\dfrac{2017+1}{2017!}-\dfrac{2018+1}{2018!}$
$\to A=\dfrac{1}{100!}+\dfrac{1}{101!}-\dfrac{1}{101!}-\dfrac{1}{102!}+..+\dfrac{1}{2016!}+\dfrac{1}{2017!}-\dfrac{1}{2017!}-\dfrac{1}{2018!}$
$\to A=\dfrac{1}{100!}-\dfrac{1}{2018!}<\dfrac{1}{100!}$
