Show that if the series converges and the series diverges, then the series diverges.
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.
Originally Posted by wopashui
Give examples to show that if and both diverge, then each of the series
may converge or may diverge
Just define to make diverge and converge, and to get it the other way around.