
Re: Alternating series question
Posted:
Apr 21, 2013 8:41 PM


"Ray Vickson" <RGVickson@shaw.ca> wrote in message news:9d4e47cde84a4af888d974bca09ebf2e@googlegroups.com... > Suppose we have an infinite series of the form sum{(1)^n * a_n} where all a_n > 0 and limit > a_n = 0 as n > infinity. However, we do NOT assume the a_n are monotone decreasing in n; we > just assume they > 0. Can we still say that the series is convergent?
1/2  1/1 + 1/4  1/2 + 1/8  1/3 + 1/16  1/4 + 1/32  1/5 + ...
is divergent, but meets your criteria. (I.e. interleaving the terms of a convergent geometric series, with the terms of the divergent harmonic series)
Mike.

