By definition the generating function of a sequence is...
In your case is...
... so that...
One more question. This section of the book is pretty spotty.
Find a closed for for the generating function for the sequence a(n) = , for n=0, 1, 2.
There is the table for generating functions and I was looking at 1/(1+x)^n but I don't really think that is correct.
Also I tried to use the math tags to make it more legible for once. Hopefully I least got that right.