$a)$ $A=\dfrac{2020}{2019}+\dfrac{2019}{2018}+\dfrac{2018}{2017}=3+\dfrac{1}{2019}+\dfrac{1}{2018}+\dfrac{1}{2017}>3$
$B=\dfrac{1}{3}+\dfrac{1}{4}+...+ \dfrac{1}{17}$
$B=(\dfrac{1}{3}+\dfrac{1}{4}+..+\dfrac{1}{7})+(\dfrac{1}{8}+\dfrac{1}{9}+..+\dfrac{1}{12})+(\dfrac{1}{13}+\dfrac{1}{14}+..+\dfrac{1}{17})$
$→$ $B<\dfrac{1}{3}\times5+\dfrac{1}{8}\times 5+\dfrac{1}{13}\times 5≈2,676<3$
$→B<A$
