Giải thích các bước giải:
Ta có :
$S=\dfrac{2}{5}+(\dfrac{2}{5})^2+(\dfrac{2}{5})^3+..+(\dfrac{2}{5})^{2020}$
$\to \dfrac{2}{5}.S=(\dfrac{2}{5})^2+(\dfrac{2}{5})^3+(\dfrac{2}{5})^4+..+(\dfrac{2}{5})^{2021}$
$\to S-\dfrac{2}{5}S=\dfrac{2}{5}-(\dfrac{2}{5})^{2021}$
$\to \dfrac{3}{5}S=\dfrac{2}{5}-(\dfrac{2}{5})^{2021}<\dfrac{2}{5}$
$\to S<\dfrac{2}{3}$