# Sums, products, and limits

```latex
\sum_{k=1}^{n} k = \frac{n(n+1)}{2}
```

```latex
\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}
```

```latex
\prod_{k=1}^{n}k=n!
```

```latex
\lim_{x\to 0}\frac{\sin x}{x}=1
```

```latex
\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n=e
```