Hölder's Inequality for Sums/Finite

Hölder's Inequality for Sums: Also presented as
Hölder's Inequality for Sums can also be seen presented in the less general form:
 * $\ds \sum \limits_{k \mathop = 1}^n \size {x_k y_k} \le \paren {\sum_{k \mathop = 1}^n \size {x_k}^p}^{1 / p} \paren {\sum_{k \mathop = 1}^n \size {y_k}^q}^{1 / q}$

where $\sequence {x_k}$ and $\sequence {y_k}$ are real sequences.

Also note that statements of Hölder's Inequality for Sums will commonly insist that $p, q > 1$.

However, from Positive Real Numbers whose Reciprocals Sum to 1 we have that if:
 * $p, q > 0$

and:
 * $\dfrac 1 p + \dfrac 1 q = 1$

it follows directly that $p, q > 1$.