$A=\dfrac{3}{1.3}+\dfrac{3}{3.5}+\dfrac{3}{5.7}+...+\dfrac{3}{2011.2013}^{}$
⇔ $\dfrac{2}{3}A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{2011.2013}^{}$
⇔ $\dfrac{2}{3}A^{}=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2011}-\dfrac{1}{2013}$
⇔ $\dfrac{2}{3}A=1-\dfrac{1}{2013}$
⇔ $\dfrac{2}{3}A=\dfrac{2012}{2013}$
⇔ $A^{}=\dfrac{1006}{671}$
Chúc bạn học tốt !!!!!
