Sum (sigma) notation disparity this might be a stupid question but I've googled it and I can't find an answer that I "trust". I am dealing with PCA (I guess that's not relevant, but just in case it is) and I am seeing a lot of Sigma notation that I'm not used to. My whole life I've always seen the following:
$\sum_{i=1}^{10}$
But now I am seeing this:
$\sum_{i}$
Does it mean exactly the same, supposing it is known that n=10 ?? 

Basically, yes.  It means that the index you are summing over is $i$, and presumably the domain for $i$ is stated elsewhere.
You might also see things like
$$ \sum_{a\in A} $$
or 
$$ \int_A $$
etc.
