Does the following series converge?
$\displaystyle \sum_{n=1}^{\infty} \frac{1}{(\log_{e} 2n)\sqrt{n}}$
here the first sequence $\displaystyle f(x) $ is monotonically decreasing, and its limits is 0 when $\displaystyle n $ tends to infinity. but the sequence $\displaystyle g(x) $ is a sequence of real numbers, but wikipedia says that for Dirichlet's test, $\displaystyle g(x)$ should be a sequence of complex numbers[/tex]
what do you say?