1/2x4 + 1/4x6 + 1/6x8 + ... + 1/2020 x2022

Đặt `A =` $\dfrac{1}{2×4}$ + $\dfrac{1}{4×6}$ + $\dfrac{1}{6×8}$ +...+ $\dfrac{1}{2020 × 2022}$

`2A =` $\dfrac{2}{2×4}$ + $\dfrac{2}{4×6}$ + $\dfrac{2}{6×8}$ +...+ $\dfrac{2}{2020 × 2022}$

`2A =` $\dfrac{1}{2}$ - $\dfrac{1}{4}$ + $\dfrac{1}{4}$ - $\dfrac{1}{6}$ + $\dfrac{1}{6}$ - $\dfrac{1}{8}$ +...+ $\dfrac{1}{2020}$ - $\dfrac{1}{2022}$

`2A =` $\dfrac{1}{2}$ - $\dfrac{1}{2022}$

`2A =` $\dfrac{1011}{2022}$ - $\dfrac{1}{2022}$

`2A =` $\dfrac{505}{1011}$

`A =` $\dfrac{505}{1011}$ `: 2`

`A =` $\dfrac{505}{2022}$

Vậy $\dfrac{1}{2×4}$ + $\dfrac{1}{4×6}$ + $\dfrac{1}{6×8}$ +...+ $\dfrac{1}{2020 × 2022}$ `=` $\dfrac{505}{2022}$