Đáp án: $B=3\dfrac14$
Giải thích các bước giải:
Ta có:
$B=\dfrac{5}{2\cdot 1}+\dfrac{4}{1\cdot11}+\dfrac{3}{11\cdot2}+\dfrac{1}{2\cdot15}+\dfrac{13}{15\cdot4}$
$\to B=\dfrac{5}{2\cdot 1}+(\dfrac{4}{1\cdot11}+\dfrac{3}{11\cdot2})+(\dfrac{1}{2\cdot15}+\dfrac{13}{15\cdot4})$
$\to B=\dfrac{5}{2}+(\dfrac{4}{11}+\dfrac{3}{22})+(\dfrac{1}{30}+\dfrac{13}{60})$
$\to B=\dfrac{5}{2}+(\dfrac{8}{22}+\dfrac{3}{22})+(\dfrac{2}{60}+\dfrac{13}{60})$
$\to B=\dfrac{5}{2}+\dfrac{8+3}{22}+\dfrac{2+13}{60}$
$\to B=\dfrac{5}{2}+\dfrac{11}{22}+\dfrac{15}{60}$
$\to B=\dfrac52+\dfrac12+\dfrac14$
$\to B=\dfrac{5+1}2+\dfrac14$
$\to B=\dfrac{6}2+\dfrac14$
$\to B=3+\dfrac14$
$\to B=3\dfrac14$
