Q:

How to get for to stand separate in an equation?

I have the following equation:
\begin{equation}
    C_k = \frac{1}{N}\sum\limits_{n=1}^N k_n           for k \in {1,\dots,K}
\end{equation}

How can I get the for, and everything after it, to stand 'separate' from the equation?

A:

You can use \quad to add a space (or \qquad if you want it bigger) and \text{} to insert some text in your equation in a way that it is not typeset in displaymath style. Remember also to insert a space right after the text with\ or to add it inside the text like \text{for }.
\begin{equation}
    C_k = \frac{1}{N}\sum\limits_{n=1}^N k_n \quad \text{for}\  k \in \{1,\dots,K\}
\end{equation}

A:

I tend to do this
\newcommand\qqtext{\qquad\text}
\begin{equation}
    C_k = \frac{1}{N}\sum\limits_{n=1}^N k_n   \qqtext{for $k \in {1,\dots,K}$}
\end{equation}

Note that I include the entire for... part inside the \qqtext{...}, because semantically this is where it belongs.
This way I ensure I always have the same distance for the conditions. I also tend to use the following macros
\newcommand\qtextq[1]{\quad\text{#1}\quad} % for 'and' between eqs
\newcommand\qtext{\quad\text}  % when there is not enough space for \qqtext

Plus possibly e versions using \enspace instead of \quad.
I tend to hide these spacings inside macros in order to make the general text easier to read (less typographic noise).

