Đáp án:
Giải thích các bước giải:
Ta có : A = $\frac{1}{2018}$ + $\frac{2}{2017}$ + $\frac{3}{2016}$ + ... + $\frac{2017}{2}$
A =( $\frac{1}{2018}$ + 1 )+( $\frac{2}{2017}$ + 1 ) + ( $\frac{3}{2016}$ + 1 ) + ... +( $\frac{2017}{2}$ + 1 ) + 1
A = $\frac{2019}{2018}$ + $\frac{2019}{2017}$ + $\frac{2019}{2016}$ + ... + $\frac{2019}{2}$ +$\frac{2019}{2019}$
A = 2019. ( $\frac{1}{2}$ + $\frac{1}{3}$ +$\frac{1}{4}$ + ... + $\frac{1}{2019}$ )
⇒ $\frac{A}{B}$ = $\frac{2019 ( \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{2019} }{\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{2019}}$
⇒ $\frac{A}{B}$ = 2019
Vậy $\frac{A}{B}$ = 2019