Giải thích các bước giải:
Ta có :
$A=\dfrac{9}{1.2}+\dfrac{9}{2.3}+\dfrac{9}{3.4}+..+\dfrac{9}{2019.2020}$
$\to A=9(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+..+\dfrac{1}{2019.2020})$
$\to A=9(\dfrac{2-1}{1.2}+\dfrac{3-2}{2.3}+\dfrac{4-3}{3.4}+..+\dfrac{2020-2019}{2019.2020})$
$\to A=9(\dfrac 11-\dfrac 12+\dfrac 12-\dfrac 13+\dfrac 13-\dfrac 14+..+\dfrac 1{2019}-\dfrac 1{2020})$
$\to A=9(1-\dfrac 1{2020})$