There is one series and it seems pretty much easy to check either it is divergent or convergent but because of the complex denominator I am not able to get the solution by the certain convergent tests. Here is the question;
$\sum _{k=0}^{\infty} \left [ (-1)^{k}(2k)!\left(\frac {1} {(i+a)^{2k+1}}-\frac {1} {(-i+a)^{2k+1}}\right) \right ]$
Does anyone have an idea about this either it is convergent or divergent? a could be any number, for large k it seems it diverges but need a way to prove it? By comperition we could get rid of from $(2n)!$ but I do not know how to compare these complex donominators.
Thank you...