The discussion revolves around the convergence or divergence of the series Ʃ (2n)!/(n-1)*3^n, starting from n=2 to infinity. Participants are exploring the application of convergence tests, particularly the ratio test and nth-term test.
Some participants have provided guidance on interpreting the results of the ratio test, specifically regarding the condition when L>1. However, there appears to be some confusion about the correct interpretation of the limit in relation to convergence and divergence.
There is a repeated emphasis on the limit obtained from the ratio test and its implications, indicating a potential misunderstanding of the convergence criteria. The discussion reflects a need for clarification on these concepts.
Alexc475 said:Homework Statement
Does The series Ʃ (2n)!/(n-1)*3^n converge or diverge?
(Starts at n=2 to infinity )
Homework Equations
The Attempt at a Solution
I tried the ratio test and nth-term test, and ended up with infinity, I'm not sure about it's convergence.
Dick said:If the ratio you get from the ratio test goes to infinity, then the series diverges.
No, if L > 1, it diverges.Alexc475 said:Ohh no wonder. Thank you! I forgot that if L>1 (L being the limit) that it converges