Ta có
$A=\dfrac{1}{2} + \dfrac{2}{3} + \cdots + \dfrac{2019}{2020} = \left( 1 - \dfrac{1}{2} \right) + \left( 1 - \dfrac{1}{3} \right) + \cdots + \left( 1 - \dfrac{1}{2020} \right)$
$= \underbrace{1 + \cdots + 1}_{2019 \, \text{số 1}} - \left( \dfrac{1}{2} + \dfrac{1}{3} + \cdots + \dfrac{1}{2020} \right)$
$= 2019 - \left( \dfrac{1}{2} + \dfrac{1}{3} + \cdots + \dfrac{1}{2020} \right)$
Ta sẽ tính
$S = \dfrac{1}{2} + \dfrac{1}{3} + \cdots + \dfrac{1}{2020}$
