An infinite indexed summation is written as $\sum\limits_{i=1}^\infty i$.
A summation of items in a set, finite or not, is $\sum\limits_{c\in C} c$.
How should I represent an infinite sum of the same thing over and over?
Is just $\sum c$ clear enough? Or…
$\sum\limits^\infty c$
$\sum\limits^\infty_{\_} c$
ps.
A more appealing example is perhaps the big X from \varprod which isn't available here.
One of the use cases is to represent a "stream" of Cartesian products that can be zipped to another, finite, one and discard the excess. Actually, the tuples will be zipped, but the result is the same anyway.
ps.2 –
It is something to be written several times in an algebraic expression. Like a language to define a system, so the less verbose the better.
Best Answer
For instance, you can write: $$ \sum_{k=0}^{\infty} c $$ (since $c$ does not depend on $k$, it is clear that you mean an infinite sum of the same element).