Đáp án:
$M =\dfrac{4024}{2013}$
Giải thích các bước giải:
$\quad M =\dfrac{4}{1.3} +\dfrac{4}{3.5} +\cdots +\dfrac{4}{2011.2013}$
$\to M = 2\left(\dfrac{2}{1.3} +\dfrac{2}{3.5} +\cdots +\dfrac{2}{2011.2013}\right)$
$\to M =2\left(\dfrac{3-1}{1.3} +\dfrac{5-3}{3.5} +\cdots +\dfrac{2013-2011}{2011.2013}\right)$
$\to M = 2\left(1-\dfrac13 +\dfrac13 -\dfrac15 +\cdots +\dfrac{1}{2011} -\dfrac{1}{2013}\right)$
$\to M = 2\left(1-\dfrac{1}{2013}\right)$
$\to M =\dfrac{2.2012}{2013}$
$\to M =\dfrac{4024}{2013}$
