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

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- March 29th 2010, 05:58 PMwopashuiProve the series is diverge
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 - March 29th 2010, 07:37 PMTinyboss
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.