A Question about the Alternating Series Test

by mscudder3
Tags: alternating series, convergence, limit
 Sci Advisor P: 3,252 Look at a sequence whose odd terms are a convergent sequence of positive terms, like a geometric series and whose even terms are the terms of the divergent harmonic series {1/n}. The alternating sequence of negative odd terms and positive even terms should diverge. Intuitively this is because what is begin taken away reaches a limit while what is being added doesn't. It will be a slight nuisance to get the indexing written correctly. I think harmonic terms will be $$\frac{1}{ (n/2)+1}$$ , for $$n = 0,2,4,...$$