Đáp án:
Vậy $A=\dfrac{1006}{2013}$
Giải thích các bước giải:
$A=\dfrac1{1.3}+\dfrac1{3.5}+\dfrac1{5.7}+…+\dfrac1{2011.2013}$
$2A=\dfrac2{1.3}+\dfrac2{3.5}+\dfrac2{5.7}+…+\dfrac2{2011.2013}$
$2A=\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5}+\dfrac{7-5}{5.7}+…+\dfrac{2013-2011}{2011.2013}$
$2A=\dfrac11-\dfrac13+\dfrac13-\dfrac15+\dfrac{1}{5}-\dfrac17+…+\dfrac{1}{2011}-\dfrac1{2013}$
$2A=\dfrac11-\dfrac1{2013}$
$2A=\dfrac{2012}{2013}$
$A=\dfrac{2012}{2013}:2$
$A=\dfrac{1006}{2013}$
Vậy $A=\dfrac{1006}{2013}$
