We finish with an overview of all common limits from this chapter.

\[\begin{aligned}\lim_{n\to\infty} n^r &= \begin{cases} 0 &\text{if } r < 0 \\ \\ 1 &\text{if } r = 0 \\ \\ \infty &\text{if } r>0\text. \end{cases}\\ \\ \lim_{n\to\infty} z^n &= 0 \text{ if } |z| < 1\\ \lim_{n\to\infty} \frac{n^k}{g^n} &=0 \text{ if } k > 0 \text{ and } g > 1\\ \\ \lim_{n\to\infty} \left( 1 + \frac{x}{n} \right)^n &= e^x\end{aligned}\]