Giải thích các bước giải:
13.Ta có:
$L=\lim\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{n(n+1)}$
$\to L=\lim\dfrac{2-1}{1.2}+\dfrac{3-2}{2.3}+...+\dfrac{n+1-n}{n(n+1)}$
$\to L=\lim\dfrac11-\dfrac12+\dfrac12-\dfrac13+...+\dfrac1n-\dfrac1{n+1}$
$\to L=\lim1-\dfrac1{n+1}$
$\to L=1-0$
$\to L=1$
14.Ta có:
$L=\lim\dfrac1{2.5}+\dfrac1{5.8}+...+\dfrac{1}{(3n-1)(3n+2)}$
$\to 3L=\lim\dfrac3{2.5}+\dfrac3{5.8}+...+\dfrac{3}{(3n-1)(3n+2)}$
$\to 3L=\lim\dfrac{5-2}{2.5}+\dfrac{8-5}{5.8}+...+\dfrac{(3n+2)-(3n-1)}{(3n-1)(3n+2)}$
$\to 3L=\lim\dfrac12-\dfrac15+\dfrac15-\dfrac18+...+\dfrac1{3n-1}-\dfrac1{3n+2}$
$\to 3L=\lim\dfrac12-\dfrac1{3n+2}$
$\to 3L=\dfrac12-0$
$\to 3L=\dfrac12$
$\to L=\dfrac16$
