Đáp án:
$\dfrac{2022}{2023}$
Giải thích các bước giải:
$\dfrac2{1\times3}+\dfrac2{3\times5}+\dfrac2{5\times7}\ +\,.\!.\!.+\ \dfrac2{2021\times2023}\\=\dfrac{3-1}{1\times3}+\dfrac{5-3}{3\times5}+\dfrac{7-5}{5\times7}\ +\,.\!.\!.+\ \dfrac{2023-2021}{2021\times2023}\\=1-\dfrac13+\dfrac13-\dfrac15+\dfrac15-\dfrac17\ +\,.\!.\!.+ \ \dfrac{1}{2021}-\dfrac1{2023}\\=1-\dfrac1{2023}\\=\dfrac{2022}{2023}$
