Understanding the nth Term Test for Divergence in Series

[kamranonline]

I have a problem understanding the divergence of series.. There is a n-th term test that u first apply on the general term of the series and if its limit is not equal 0 then the series is divergent.. When i apply that test sometime i get it wrong and sometime not.. When can i apply this test? is there any special conditions for it? or it should always work.

 

[Tedjn]

Please show us examples of what you mean by getting it wrong. The nth term test can tell you if a series diverges, but not all series that diverge fail the nth term test.