infinite series (alternating series test)...need help

[lotus776]

Part of testing for divergence/convergence involves the use of the "Alternating Series Test". I need to prove that a series is both DECREASING and the limit -> 0. I obviously know how to test the limit (which I usually do first) but determining if the series is decresing or not is harder to prove. The simple answer is to look at the denominator and if it "larger" than the numerator than the series is decreasing but my teacher says that is not a sufficient proof.
Please explain how to prove that a series is decreasing

thanks