<s>[INST] How do I determine the limit of this sequence? I need a refresher. 
I would assume that the answer would be $\infty$, but I am not quite sure.
The problem reads: 
Determine the limit of this sequence? $c_n$ = $\sqrt {n^2+n} - \sqrt {n^2 - n}$ .
I would need a refresher on this. That's all thank you. 
 [/INST] $$\begin{align*}
c_n &= \frac{\left(\sqrt{n^2+n}-\sqrt{n^2-n}\right)\left(\sqrt{n^2+n}+\sqrt{n^2-n}\right)}{\sqrt{n^2+n}+\sqrt{n^2-n}}\\
&= \frac{n^2+n-n^2+n}{\sqrt{n^2+n}+\sqrt{n^2-n}}\\
&= \frac{2n}{\sqrt{n^2+n}+\sqrt{n^2-n}}\\
&= \frac{2}{\sqrt{1+1/n}+\sqrt{1-1/n}}\\
&\to \frac{2}{\sqrt{1+0}+\sqrt{1-0}}\\
&= 1
\end{align*}$$
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