Summations manipulation: is this one right?

Question

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

Since the $p_l$ is not dependent on the innermost summation index, it should be fine... — J. M. ain't a mathematician, Jul 07 '12 at 14:18

score 1 · Accepted Answer · answered Jul 07 '12 at 14:16

1

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.

answered Jul 07 '12 at 14:16

Thomas

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Summations manipulation: is this one right?

1 Answers1