Can some one help me with this question?

Use the Dirichlet test to show that the series

.

converges for all

with

but

.

I know that the Dirichlet test for the convergence of a series of complex numbers can be stated as follows:

Suppose that

is a sequence of positive real numbers with

for all

and

= 0. Suppose that

is a sequence of complex numbers so that there exists

so that, for all

,

.

(Upper limit in that sum should be N, not infty.) Then the series

converges.

So how do I start? Just really confused. Do I let

and start from there?

Yes !