Giải thích các bước giải:
Ta có:
$A=\dfrac1{2.9}+\dfrac1{9.7}+...+\dfrac1{252.509}$
$\to A=\dfrac{2}{4.9}+\dfrac{2}{9.14}+...+\dfrac{2}{504.509}$
$\to A=\dfrac25(\dfrac{5}{4.9}+\dfrac{5}{9.14}+...+\dfrac{5}{504.509})$
$\to A=\dfrac25(\dfrac{9-4}{4.9}+\dfrac{14-9}{9.14}+...+\dfrac{509-504}{504.509})$
$\to A=\dfrac25(\dfrac14-\dfrac19+\dfrac19-\dfrac1{14}+...+\dfrac1{504}-\dfrac1{509})$
$\to A=\dfrac25(\dfrac14-\dfrac1{509})$
