25.16. Calculate $\lim _{n \rightarrow \infty}\left(\sqrt{n^{2}+n}-n\right)$.
25.16. Answer: 1/2. By multiplying and dividing $\sqrt{n^{2}+n}-n$ by $\sqrt{n^{2}+n}+n$, we get

$$
\sqrt{n^{2}+n}-n=\frac{n}{\sqrt{n^{2}+n}+n}=\frac{1}{\sqrt{1+\frac{1}{n}}+1} \rightarrow \frac{1}{2}
$$