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

**Runty** · March 29th 2010, 10:18 AM

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.

**Krizalid** · March 29th 2010, 10:27 AM

easy example, put $a_n=b_n=\frac1n.$

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

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