Question: Given any series (an, we define a series whose terms are all the positive terms of ( an and a series whose terms are all

Given any series (an, we define a series whose terms are all the positive terms of ( an and a series whose terms are all the negative terms of (an. to be specific, we let

If an > 0, then and whereas if an and
(a) If (an is absolutely convergent, show that both of the series and are convergent.
(b) If (an is conditionally convergent, show that both of the series and are divergent.

a;- an + lal 2 ai-a,2141 an an an-0

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