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)
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?