Đáp án:
$a = -2$
Giải thích các bước giải:
Sửa đề: $\lim(\sqrt{n^2 + an + 5} -\sqrt{n^2 +1})$
$=\lim\dfrac{((\sqrt{n^2 + an + 5} -\sqrt{n^2 +1})(\sqrt{n^2 + an + 5} +\sqrt{n^2 +1})}{\sqrt{n^2 + an + 5} +\sqrt{n^2 +1}}$
$=\lim\dfrac{n^2 + an+ 5 - (n^2 +1)}{\sqrt{n^2 + an + 5} +\sqrt{n^2 +1}}$
$=\lim\dfrac{an + 4}{\sqrt{n^2 + an + 5} +\sqrt{n^2 +1}}$
$=\lim\dfrac{a +\dfrac4n}{\sqrt{1 +\dfrac an +\dfrac{5}{n^2}} +\sqrt{1+\dfrac{1}{n^2}}}$
$=\dfrac{a +0}{\sqrt{1 +0+0} +\sqrt{1+0}}$
$=\dfrac{a}{2}$
Lại có:
$\lim un_n = -1$
$\to \dfrac a2 = -1$
$\to a = -2$
