Ratio and Root Test series problem.
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.