Series Laws and Theorems and how they affect each other

[kylera]

Is it mathematically possible for a series to be first declared "possibly not divergent" via the Test For Divergence, then to be declared divergent by applying the Integral Test?

On that tangent, does that mean that the Test For Divergence will only render the conclusions "definitely divergent" and "inconclusive"? Much thanks in advance.

 

[sour_kremlin]

Yes to both questions.

For example, the harmonic series 1/n doesn't diverge via the Test for Divergence, but it is divergent.