This question is about the alternating series test. That says an alternating series converges if the limit is 0 AND it is decreasing BUT wouldn't this be true regardless of whether or not the series is alternating?
I assume not accept I am having trouble thinking of an examples and thought someone would be kind enough to show an example of a series that has a limit of 0 and is decreasing but is not converging due to the fact that it is not alternating.
Note that for $\sum a_n$ the condition $a_n\to 0$ is a necessary but not sufficient condition.
The classical example is of course given by the harmonic series $\sum \frac1n$.