$\dfrac{6}{1.4}$ $+$ $\dfrac{6}{4.7}$ $+$ $.....$ $+$ $\dfrac{6}{2017.2020}$
$=$ $2$$.$ $($ $\dfrac{3}{1.4}$ $+$ $\dfrac{3}{4.7}$ $+$ $.....$ $+$ $\dfrac{3}{2017.2020}$ $)$
$=$ $2$ $.$ $($ $1$ $-$ $\dfrac{1}{4}$ $+$ $\dfrac{1}{4}$ $-$ $\dfrac{1}{7}$ $+$ $.....$ $+$ $\dfrac{1}{2017}$ $-$ $\dfrac{1}{2020}$ $)$
$=$ $2$ $.$ $($ $1$ $-$ $\dfrac{1}{2020}$ $)$
$=$ $2$ $.$ $\dfrac{2019}{2020}$
$=$ $\dfrac{4038}{2020}$
$=$ $\dfrac{2019}{1010}$
Vậy $A$ $=$ $\dfrac{2019}{1010}$
Học tốt nha!
