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Are there general rules that apply? For example:

(convergent series) + (divergent series) = (divergent series)

(convergent series) * (divergent series) = (convergent series)

etc.

Are there steadfast rules like this? Or does it vary depending on the specific series?

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    For multiplication, you may be interested in [Dirichlet's test for convergence](http://en.wikipedia.org/wiki/Dirichlet's_test).2012-05-19

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