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Math Help - Give examples to show that the following series may converge or diverge

  1. #1
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    Give examples to show that the following series may converge or diverge

    Give examples to show that if \sum a_k and \sum b_k both diverge, then each of the series \sum (a_k+b_k) and \sum (a_k-b_k) may converge or diverge.

    I'm not 100% sure how to complete this, though I was advised to use \sum_{k=1}^{\infty}1, which is divergent. I'm not quite sure how to use this, though.

    I think for the first one, if I have b_k=-a_k, then I can show it is convergent since \sum (a_k+(-a_k))=0. This could also work for the second one if I just have b_k=a_k.

    I've probably got better answers than I think I do, but I could use a second opinion in any case.
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  2. #2
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    Krizalid's Avatar
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    easy example, put a_n=b_n=\frac1n.
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