# Summations manipulation: is this one right?

I've got a summation like this:

$\sum_{l=1}^L \sum_{i=1}^I p_l c_l^i = \sum_{l=1}^L \sum_{i=1}^I p_l w_l^i$

Is it right to bring $p_l$ out of the symbol $\sum_{i=1}^I$ such that:

$\sum_{l=1}^L p_l \sum_{i=1}^I c_l^i = \sum_{l=1}^L p_l \sum_{i=1}^I w_l^i$ ?

Thank you in advance

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Since the $p_l$ is not dependent on the innermost summation index, it should be fine... –  Ｊ. Ｍ. Jul 7 '12 at 14:18

Yes that is correct. Since the $p_l$ does not depend on $i$, you can bring it out. For a fixed $l$ the $p_l$ is just a common factor of all the terms in the sum $\sum_{i=1}^I$ where $i$ varies.