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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
up vote 1 down vote accepted

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.

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