The discussion revolves around the convergence or divergence of the series Ʃ1/(1+2+3+4+5...+n) as n approaches infinity. Participants are exploring the implications of rewriting the series and comparing it to known divergent series.
The discussion is active, with participants questioning their assumptions and exploring different interpretations of the series. Some guidance has been offered regarding the formula for the sum of integers, which has prompted further reflection on the original problem.
There is a focus on the mathematical properties of series and the need to clarify the assumptions underlying the convergence or divergence of the given series. Participants are also considering the implications of rewriting the series in different forms.
Nikitin said:Homework Statement
Does this converge or diverge?
Ʃ1/(1+2+3+4+5...+n), as n---> infinity?
The Attempt at a Solution
I rewrote this into Ʃ(Ʃ1/n) (is it correct?).
I figured that since Ʃ(1/n) diverges, then the sum of each partial sum most (obviously) also diverge.
However, it appears I'm mistaken. Can somebody help?