How to write Latex symbol norm vector or value ?

How to write Latex symbol norm for frac?

How to write Latex symbol norm for sum?

\lVert and \rVert

Latex symbol norm of a vector or a value

$$\lVert \vec{x} \rVert$$
\[\lVert \vec{x} \rVert\] 
$$\lVert \cos x \rVert$$
\[\lVert \cos x \rVert\]

Adjust Latex norm for frac

$$\left\lVert \frac{1}{x} \right\rVert$$
\[\left\lVert \frac{1}{x} \right\rVert\]

Adjust Latex symbol norm for sum

$$\left\lVert \sum_{k=1}^n \alpha_k\right\rVert$$
\[\left\lVert \sum_{k=1}^n \alpha_k\right\rVert\]