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Latex norm for vector and sum

How to write Latex norm vector or value ?
How to write Latex norm for frac?
How to write Latex norm for sum?
\lVert and \rVert

Latex norm of a vector or a value

\lVert 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 norm for sum

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

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

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