Đáp án:
$\dfrac{126}{172}$
Giải thích các bước giải:
$A=\dfrac3{1.5}+\dfrac3{5.9}+\dfrac3{9.13}\ +\,.\!.\!.+\ \dfrac{3}{39.43}\\\Rightarrow \dfrac A3=\dfrac{1}{1.5}+\dfrac{1}{5.9}+\dfrac1{9.13}\ +\,.\!.\!.+\ \dfrac{1}{39.43}\\\Rightarrow \dfrac{4A}{3}=\dfrac{4}{1.5}+\dfrac{4}{5.9}+\dfrac4{9.13}\ +\,.\!.\!.+\ \dfrac{4}{39.43}\\\Rightarrow \dfrac{4A}{3}=1-\dfrac15+\dfrac15-\dfrac19+\dfrac19-\dfrac1{13}\ +\,.\!.\!.+\ \dfrac{1}{39}-\dfrac{1}{43}\\\Rightarrow \dfrac{4A}{3}=1-\dfrac{1}{43}\\\Rightarrow \dfrac{4A}{3}=\dfrac{42}{43}\\\Rightarrow 4A=\dfrac{126}{43}\\\Rightarrow A=\dfrac{126}{172}$
Vậy biểu thức có giá trị là $\dfrac{126}{172}$.
