The discussion revolves around finding an example of a convergent series \(\Sigma z_{n}\) where the limit superior of the absolute ratio of consecutive terms exceeds 1. Participants are exploring the properties of series convergence and the implications of the ratio test.
The discussion is active, with participants sharing ideas and questioning the validity of their approaches. There is an acknowledgment of the potential issue with the limit superior in the proposed method, suggesting a productive exploration of the topic.
Participants are working under the constraint of providing an example that meets specific criteria regarding the limit superior of the series terms, which may influence their reasoning and suggestions.
gas8 said:yeah thx, I used 2^(-n) when n is even and 2^-(n+1 ) when n is odd