`A = 4/35 + 4/63 + 4/99 .... + 4/255`

$\text{→ Đáp án + Giải thích các bước giải:}$

$\text{→ Ta có :}$

$\text{A = $\dfrac{4}{35}$ + $\dfrac{4}{63}$ + . . + $\dfrac{4}{255}$}$

$\text{⇔ $\dfrac{A}{2}$ = $\dfrac{2}{35}$ + $\dfrac{2}{63}$ + . . + $\dfrac{2}{255}$}$

$\text{⇔ $\dfrac{A}{2}$ = $\dfrac{2}{5 . 7}$ + $\dfrac{2}{7 . 9}$ + . . + $\dfrac{2}{15 . 17}$}$

$\text{⇔ $\dfrac{A}{2}$ = $\dfrac{1}{5}$ - $\dfrac{1}{7}$ + $\dfrac{1}{7}$ - . . - $\dfrac{1}{17}$}$

$\text{⇔ $\dfrac{A}{2}$ = $\dfrac{1}{5}$ - $\dfrac{1}{17}$}$

$\text{⇔ A = 2 . $\dfrac{12}{85}$ = $\dfrac{24}{85}$.}$

$\text{→ Vậy A = $\dfrac{24}{85}$.}$

$\color{red}{\text{ThieuNangLamToanHoc}}$