This is a problem on an exam review sheet for a discrete mathematics course.
Consider a generating function
Using operations on generating functions, obtain a generating function for the sequence $a_0, a_2, a_4, a_6, ..., a_k$ .
I guess I'm just kind of confused as to what exactly I'm supposed to find. Would I need to find a way to subtract the odd power terms in $F(x)$, or do I find a function of the form
If I already wrote out this function is it given or do I need to somehow put it in terms of $F(x)$? Sorry if this is a silly question, I'm sure if I just figure out what I'm supposed to be finding I can figure out the rest on my own.