limit of $a_n=\sqrt{n^2+2} - \sqrt{n^2+1}$ as $n$→∞ $a_n=\sqrt{n^2+2} - \sqrt{n^2+1}$ as $n$→∞
Both limits tend to infinity, but +∞ −(+∞) doesn't make sense. How would I get around to solving this?

We have $$\lim_{n \to \infty }\sqrt{n^2+2} - \sqrt{n^2+1} = \lim_{n \to \infty} = \frac{n^2+2 - n^2-1}{\sqrt{n^2+2} + \sqrt{n^2+1}} = \lim_{n \to \infty} \frac{1}{\sqrt{n^2+2} + \sqrt{n^2+1}}\\ = \lim_{n \to \infty}\frac{1}{n} \lim_{n \to \infty} \frac{1}{\sqrt{1+\frac{2}{n^2}} + \sqrt{1+\frac{1}{n^2}}} = \frac{1}{2}\lim_{n \to \infty} \frac{1}{n}= 0$$
