Intersection on a range

Like this?

\begin{displaymath}
  \bigcap\limits^n_{i=0}
\end{displaymath}

If you want to use it as inline math you could write it like this:

$\bigcap^n_{i=0}$

Since it's a very large symbol I wouln't suggest the inline solution

Here is a solution creating the output you described

{\bigcap}_{i=0}^k