Đáp án+Giải thích các bước giải

`3/{2×4} + 3/{4×6} + 3/{6×8} + ... + 3/{18×20}`

`=` `2/3(2/{2×4} + 2/{4×6} + 2/{6×8} + ... + 2/{18×20})`

`=` `2/3(1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/18 - 1/20)`

`=` `2/3(1/2 - 1/20)`

`=` `2/3 × 9/20`

`=` `3/10`

Gọi biểu thức sau là`: A`

`A =` $\dfrac{3}{2 × 4}$ `+` $\dfrac{3}{4 × 6}$ `+` $\dfrac{3}{6 × 8}$ `+ .... +` $\dfrac{3}{18 × 20}$

`A : 3 × 2 =` $\dfrac{2}{2 × 4}$ `+` $\dfrac{2}{4 × 6}$ `+` $\dfrac{2}{6 × 8}$ `+ .... +` $\dfrac{2}{18 × 20}$

` =`$\dfrac{4 - 2}{2 × 4}$ `+` $\dfrac{6 - 4}{4 × 6}$ `+` $\dfrac{8 - 6}{6 × 8}$ `+ ....+` $\dfrac{20 - 18}{18 × 20}$

`=` $\dfrac{4}{2 × 4}$ `-` $\dfrac{2}{2 × 4}$ `+` $\dfrac{6}{4 × 6}$ `-` $\dfrac{4}{4 × 6}$ `+` $\dfrac{8}{6 × 8}$ - $\dfrac{6}{6 × 8}$ `+ .... +` $\dfrac{20}{18 × 20}$ `-` $\dfrac{18}{18 × 20}$

`=` $\dfrac{1}{2}$ `-` $\dfrac{1}{4}$ `+` $\dfrac{1}{4}$ `-` $\dfrac{1}{6}$ `+` $\dfrac{1}{6}$ `-` $\dfrac{1}{8}$ `+ .... +` $\dfrac{1}{18}$ `-` $\dfrac{1}{20}$

 `=` $\dfrac{1}{2}$ `-` $\dfrac{1}{20}$

`A : 3 × 2 =` $\dfrac{9}{20}$

` A =` $\dfrac{9}{20}$ `: 3 × 2`

`A = `$\dfrac{6}{20}$ `=` $\dfrac{3}{10}$

Vậy biểu thức trên có giá trị là: $\dfrac{3}{10}$

$\text{#lknhatminh0322}$