The discussion revolves around the convergence of the series given by the sum from n=0 to infinity of (3^n)/(n+1)^n. Participants are exploring the applicability of the ratio test and the root test for this series in the context of exam preparation.
The discussion is ongoing, with participants sharing their findings from the ratio and root tests. Some guidance has been offered regarding the simplicity of the root test in this case, but no consensus has been reached on the conclusions drawn from the tests.
Participants are preparing for an exam, which may impose specific constraints on the methods they can use. There is also a focus on understanding the implications of applying different convergence tests.
cue928 said:I am doing the following practice problem in prep for an exam:
sum from n=0 to infinity: (3^n)/(n+1)^n
The book says to use the ratio test on it, which I did, but would the root test also apply to this?
cue928 said:I got lim n approaches infinity 3/1+n = 0.