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Lately I came upon sums with boundaries other sums:
$\sum_{i=1}^{\sum_{j=1}^{X}p_j}q_i$
Where X can also be a sum (with a boundary of sum) etc.
I wanted to ask what kind of mathematics should I use to simplify or transform these sums in other formats (if possible) because I have no idea how to deal with them.

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    $\sum_{j=1}^{X}p_j$ is just a number (or perhaps a random variable if $X$ also is), so one approach would be to calculate it first.2012-08-06
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    I cannot do that because in the general case I theoretically can have an infinite tower of sums... Assuming that the boundary has a value (which will eventually have) is just hiding the complexity behind a symbol.2012-08-06

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