Here it is:
Show that the ratio test is inconclusive but the root test indicates convergence for the series:
(1/2) + 1/(3^2) + 1/(3^4) + 1/(2^5) + . . .
The problem I'm having here isn't necessarily the application of the ratio and root tests. Rather, I'm having trouble recognizing any sort of pattern in this series so I can get started! It should be pretty simple if I can somehow acquire an expression for the "nth" term in the series...
Any and all help is greatly appreciated.
I found that the ratio test was inconclusive quite easily, but now I'm having trouble getting the "nth" term into the form (an)^n in order to apply the root test. I can get each of the individual sum terms into that form, but it doesn't seem as if that helps get me anywhere.