Giải thích các bước giải:
$\lim \dfrac{1}{1.2}+\dfrac{1}{2.3}+..+\dfrac{1}{n(n+1)}$
$=\lim \dfrac{2-1}{1.2}+\dfrac{3-2}{2.3}+..+\dfrac{n+1-n}{n(n+1)}$
$=\lim\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+..+\dfrac{1}{n}-\dfrac{1}{n+1}$
$=\lim 1-\dfrac{1}{n+1}$
$=1$