sum(n=1..infty) 1/z^n = 1/(z-1) for |z|>1.

Put z=3exp(i theta), then we have:

sum(n=1..infty) (1/3^n) exp(-i theta) = 1/[3 exp(i theta)-1]

Now take real parts so:

Re sum(n=1..infty) (1/3^n) exp(-i n theta) = Re 1/[3 exp(i theta)-1]

or:

sum(n=1..infty) (1/3^n) cos(n theta) = Re 1/[3 exp(i theta)-1]

So now just find the real part of the Right Hand Side to complete the

problem.

RonL