Đáp án: $A=\dfrac5{14}$
Giải thích các bước giải:
Ta có:
$A=\dfrac{5}{6.8}+\dfrac{1}{2.8}+...+\dfrac{1}{8.42}$
$\to A=\dfrac{5}{6.8}+\dfrac{5}{5.2.8}+...+\dfrac{5}{5.8.42}$
$\to A=\dfrac{5}{6.8}+\dfrac{5}{10.8}+...+\dfrac{5}{40.42}$
$\to A=\dfrac{5}{6.8}+\dfrac{5}{8.10}+...+\dfrac{5}{40.42}$
$\to A=\dfrac52(\dfrac{2}{6.8}+\dfrac{2}{8.10}+...+\dfrac{2}{40.42})$
$\to A=\dfrac52(\dfrac{8-6}{6.8}+\dfrac{10-8}{8.10}+...+\dfrac{42-40}{40.42})$
$\to A=\dfrac52(\dfrac16-\dfrac18+\dfrac18-\dfrac1{10}+...+\dfrac1{40}-\dfrac1{42})$
$\to A=\dfrac52\cdot (\dfrac16-\dfrac1{42})$
$\to A=\dfrac5{14}$
