More p.m.f [p.d.f.] questions!

I think I have the hang of this now, but I have a minor question:

I am to find the constant which would make satisfy all the conditions of being a p.m.f.

I assumed that this would continue on to infinity [for there was another similar to this, where it explicitly said that ]

So, I figured that ;

I also noticed that . The series is geometric, where , and . Thus, it converges to

So for

However, my text tells me that the answer is 3.

Maybe I'm overlooking one simple thing...wait!

How do I apply the last property of a p.m.f:

to this problem?

I'd appreciate any input! :D

--Chris