(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove or disprove:

There exist series [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] so that:

1) you can get [tex] b_n [/tex] by rearranging the elements of [tex] a_n [/tex]

2) [tex]\sum b_n = 2 + \sum a_n [/tex]

3) [tex]\sum |b_n| = 2 \sum a_n [/tex]

(all the series converge to finate values)

2. Relevant equations

3. The attempt at a solution

From (1) I know that [tex]\sum |b_n| = \sum |a_n| [/tex] but I can't see how can to continue from here, can someone point me in the right direction?

Thanks.

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# Series question

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