- #1

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- Homework Statement
- > Rudin 3.4. Calculate ##\lim\limits_{n \to \infty} \left(\sqrt{n^2 + n} - n\right)##.

- Relevant Equations
- N/A

My attempt:

\begin{align}

\lim\limits_{n \to \infty} \sqrt{n^2 + n} - n &= n\sqrt{1+\frac{1}{n}} -n\\

&=n - n\\

&= 0\\

\end{align}

I think the issue is at (1)-(2)

For comparison, here is Rudin's solution

\begin{align}

\lim\limits_{n \to \infty} \sqrt{n^2 + n} - n &= n\sqrt{1+\frac{1}{n}} -n\\

&=n - n\\

&= 0\\

\end{align}

I think the issue is at (1)-(2)

For comparison, here is Rudin's solution