Here is a brief description of the different commands you tried to use:
Only
This is used either \only<x>{}, \only<x-z>{} or \only<x,y>{} and will output what is between {} only on the slide(s) (resp.) x, x to z or x and y. It does not allocate some sort of space for what is between the {} on the other slide so that
\begin{frame}{only}
\only<1>{\begin{block}{block 1}
block 1
\end{block}}
\only<2>{\begin{block}{block 2}
block 2
\end{block}}
\only<3>{\begin{block}{block 3}
block 3
\end{block}}
\end{frame}
produces:
Pause
\pause is a command used to add a pause to the frame you are building. It means that everything that is placed before the pause will be displayed on the first slide corresponding to the frame and everything that follows (but before the next \pause command if you use more than one on the same frame) will be displayed on the next slide corresponding to the frame.
It can be seen as if you were saying to Beamer, here I want you to stop the slide and wait for me to press a key before you output the following on the next slide without removing what is before.
This feature is very useful when unrevealing items from a list if you need to add some comment about the items and you don't want the audience to see the next items while you are dealing with the previous one.
Here is your code:
\begin{frame}{pause}
\begin{block}{block 1}
block 1
\end{block}
\pause
\begin{block}{block 2}
block 2
\end{block}
\pause
\begin{block}{block 3}
block 3
\end{block}
\end{frame}
and its output:
Uncover
This command can be used either like \uncover<x->{}, \uncover<x-z>{} or \uncover<x>{} and will output what is between the {} from the (resp.) x to the end slides, the x to z slides, only on the x slide.
On the illustration below you can see that even if the part between the {} is hidden, some space is allocated to it and will not be used to display something else (to compare with the only command)
Here is an example
\begin{frame}{uncover}
\uncover<1->{\begin{block}{block 1}
block 1
\end{block}}
\uncover<2>{\begin{block}{block 2}
block 2
\end{block}}
\uncover<3>{\begin{block}{block 3}
block 3
\end{block}}
and its output:
General comments
It exists a lot of other ways to reveal, overwrite, overlay and so on. parts of slides using Beamer. This is just simple explanations using the most common ones. One should add to these list the \item<x> and other derivatives from this one used to reveal sequentially the items of a list (more or less the same goal as pause but with more control if you to remove something which has been displayed).
I hope this helps for your purpose and I think you are looking for the \only command according to the description you made in your question. If not please clarify it.
The command \vphantom in useful in this case. It will reserve the vertical space required by the sum and thus prevent "wobbling" of the formula during overlays.
\documentclass{beamer}
\begin{document}
\begin{frame}{Title}
Something before\\
\bigskip
$%
B\left(%
\only<1>{A_2[i]}%
\only<2>{A_L[i]}%
\right) =%
\only<1>{C_1 + C_2 \vphantom{\displaystyle\sum_{k=1}^{L} C_k}}%
\only<2>{\displaystyle\sum_{k=1}^{L} C_k}%
\quad \text{text here }%
\only<1>{a,b,c,}%
\only<2>{a,b,c,\ldots,z}
$
\end{frame}
\end{document}
Best Answer
For fun, here's a very quick mock up of a tikz replacement. Still needs tweaking, obviously.
Clearly, I have too much time on my hands. Here's a customisable tikz-y replacement for
epsdice:This uses the trick of optional arguments from over here. The mandatory argument is the number and the optional argument takes one of two keys
line colour=<colour>anddot colour=<colour>where<colour>is any colour tikz recognises.