If ak>=0 for all k in N, and Σak= prove that Σa'k= for any rearrangement Σa'k of Σak
I think I understand this proof, I'm just having trouble making it rigorous. I was going to go the route that since ak is positive, then its sum is monotone increasing. In order to be convergent it would need to be bounded, so I can assume it's unbounded since it diverges. Then any rearrangement of the series is also going to be unbounded and then it will diverge. Is that correct thinking?