Show that if the series converges and the series diverges, then the series diverges.
Give examples to show that if and both diverge, then each of the series
and
may converge or may diverge
Suppose converges to L and converges to K. For any , there exist integers N, M so that whenever n>N and whenever n>M. Then since , we have whenever n>max(N,M), contradicting the divergence of that series.
Just define to make diverge and converge, and to get it the other way around.