Đáp án:
$\dfrac{224}{65}$
Giải thích các bước giải:
$\dfrac{7}{1.3} + \dfrac{7}{3.5} + \cdots + \dfrac{7}{61.63} + \dfrac{7}{63.65}$
$= \dfrac{7}{2}\cdot \left(\dfrac{2}{1.3} + \dfrac{2}{3.5} + \cdots + \dfrac{2}{61.63} + \dfrac{2}{63.65}\right)$
$= \dfrac{7}{2}\cdot \left(\dfrac{3 -1}{1.3} + \dfrac{5-3}{3.5} + \cdots + \dfrac{63-61}{61.63} + \dfrac{65-63}{63.65}\right)$
$= \dfrac{7}{2}\cdot \left(\dfrac{3}{1.3} - \dfrac{1}{1.3} + \dfrac{5}{3.5} -\dfrac{3}{3.5} + \cdots + \dfrac{63}{61.63}-\dfrac{61}{63.65}+ \dfrac{65}{63.65} - \dfrac{63}{63.65}\right)$
$= \dfrac{7}{2}\cdot \left(1 - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{5} +\cdots + \dfrac{1}{61} -\dfrac{1}{63}+ \dfrac{1}{63}-\dfrac{1}{65}\right)$
$= \dfrac{7}{2}\cdot\left(1 - \dfrac{1}{65}\right)$
$=\dfrac{7}{2}\cdot \dfrac{64}{65}$
$= \dfrac{224}{65}$
