Question: Why the Maple only can't calculate the sum for certain range?

Here is an example I have,

> evalf(sum(Zeta(p-2.)*2.9^p/GAMMA(.5000000000*p+1.), p = 4 .. infinity))

The Maple just returns me the same expression, but if I change the number "2.9" to be some other numbers (roughly >3 or <2.8), then Maple "will" give me the answers. What happened? Can anyone tell me why Maple refuse to do the work during that range of value (roughly between 2.8 to 3). It's even weird. If you change the initial index of the sum from "p=4" to any other bigger number, then Maple will give you the answer. But to change "2.9" to some bigger number, like 3.1, it will strike again.

Actually, that series is a convergent series, but Maple will answer "Float(infinity)" for changing "2.9" to bigger than 7. I don't blame the maple can't calculate convergent infinity sum of very big numbers, but why for some specific small range? Of course, I can calculate the partial sum to find close convergent value. 

Thanks,

YC