In my opinion, I still believe that sum of two divergence series can be convergence series.
But here is my proof:
First, we have an obvious result: sum of two convergence series is convergence series.
Take opposite of this statement is: if exist one series is (non-convergence) so cannot be (non-convergence)
$==>$ if exist one series is divergence, so sum always be divergence.!!! (because non-convergence series is divergence series and vice verse)
If my proof is wrong, please tell me where and give me an example that sum of two divergence series can be convergence series please.