Convergence/divergence of complex series

[freddyfish]

The question is simple:

how do I prove that the following series is divergent? That it is not absolutely convergent is not hard to see, but that is not enough to prove divergence of the series as it is presented:

\sum(-i)ⁿ/ln(n)

The summation is from 2 to infinity.

Thanks

 

[Dick]

The question is simple:

how do I prove that the following series is divergent? That it is not absolutely convergent is not hard to see, but that is not enough to prove divergence of the series as it is presented:

\sum(-i)ⁿ/ln(n)

The summation is from 2 to infinity.

Thanks

I don't think it is divergent. The real and imaginary parts form two alternating series, don't they?

 

[freddyfish]

Yeah, they sure do and by the Leibniz theorem they converge to some finite number. The book that the answer is taken from stinks in the sense that the key is very often wrong, so I guess this is one of the cases where it is wrong and now I also have a second opinion to take into consideration.

Thank you for your answer! :)