How to write Latex absolute value ?

How to write Latex absolute value for frac?

How to write Latex absolute value for sum?

\lvert and \rvert

Latex absolute value \lvert \rvert

$$\lvert x \rvert$$
\[\lvert x \rvert\] 
$$\lvert \cos x \rvert$$
\[\lvert \cos x \rvert\]

Latex absolute value for frac

$$\displaystyle\left\lvert \frac{1}{x} \right\rvert$$
\[\displaystyle\left\lvert \frac{1}{x} \right\rvert\]

Latex absolute value for sum

$$\displaystyle\left\lvert \sum_{k=1}^n \alpha_k\right\rvert$$
\[\displaystyle\left\lvert \sum_{k=1}^n \alpha_k\right\rvert\]