So sánh A = `1/6 + 2/15 + 3/40 + 4/96 + 5/204 + 6/391` với `11/23`

$\text{Ta có:}$

$\text{A}$ `= 1/6 + 2/15 + 3/40 + 4/96 + 5/204 + 6/391`

$\text{A}$ `=` $\dfrac{1}{2×3}$  `+`  $\dfrac{2}{3×5}$  `+`  $\dfrac{3}{5×8}$  `+`  $\dfrac{4}{8×12}$  `+` $\dfrac{5}{12×17}$  `+`  $\dfrac{6}{17×23}$

$\text{A}$ `= 1/2 - 1/3 + 1/3 - 1/5 + 1/5 - 1/8 + 1/8 - 1/12 + 1/12 - 1/17 + 1/17 - 1/23`

$\text{A}$ `= 1/2 - 1/23`

$\text{A}$ `= 21/46`

$\text{Quy đồng}$: `11/23 = 22/46` $\text{mà}$ `22/46 > 21/46`

$\text{Vậy A <}$ `11/23`

$\text{@Huong}$