latex summation code example

Example 1: how to do limits in latex

$\lim_{x \to +\infty} f(x)$

Example 2: latex sum

Inside text: $\sum_{n=1}^{\infty} 2^{-n} = 1$
On its own line: $$\sum_{n=1}^{\infty} 2^{-n} = 1$$

Example 3: integral latex

$\int_0^{2a}{\cos(x)dx}$