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Let $a= \sum_{n \geq 1}a_n $and $b=\sum_{n \geq 1}b_n$. When can I say that $$a+b = \sum_{n \geq 1}a_n + b_n$$ ?

What if all the terms were positive? Or do I need some absolute convergence?

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    Recall that a series is merely the limit of a sequence. When is the sum of the limits equal to the limit of the sum? – Git Gud Jul 08 '15 at 16:16
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    Always... I thought there is a way to rearrange the series to make $\sum a_n + b_n$ but I think this would require $\sum a_n + b_{f(n)}$. Thanks – QuestionAnswer Jul 08 '15 at 16:20
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    You don't need to rearrange it. You just need to add their partial sums. So it is valid, if both series converge. – user251257 Jul 08 '15 at 16:56

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