Giải thích các bước giải:
$L=\lim(a\sqrt{n+1}-b\sqrt{n+2}+c\sqrt{n+3})$
$=\lim\sqrt{n}.(a\sqrt{1+\dfrac1n}-b\sqrt{1+\dfrac2n}+c\sqrt{1+\dfrac3n})$
$=\lim\sqrt{n}.(a-b+c)$
Nếu $a-b+c>0\to L=+\infty$
$a-b+c<0\to L=-\infty$
$a-b+c=0\to b=a+c$
$\to L=\lim(a\sqrt{n+1}-(a+c)\sqrt{n+2}+c\sqrt{n+3})$
$\to L=\lim(a\sqrt{n+1}-a\sqrt{n+2}+c\sqrt{n+3}-c\sqrt{n+2})$
$\to L=\lim(a(\sqrt{n+1}-\sqrt{n+2})+c(\sqrt{n+3}-\sqrt{n+2}))$
$\to L=\lim(a.\dfrac{n+1-n-2}{\sqrt{n+1}+\sqrt{n+2}}+c.\dfrac{n+3-n-2}{\sqrt{n+3}+\sqrt{n+2}})$
$\to L=\lim\dfrac{-a}{\sqrt{n+1}+\sqrt{n+2}}+\dfrac{c}{\sqrt{n+3}+\sqrt{n+2}}$
$\to L=0$
