Math Help - Generating function help plz

1. Generating function help plz

Hi, I am encountering this problem:

Let a0, a1, a2.... be an infinite sequence of non-negative integers and A(x) = the summation of an * x^n is the corresponding generating function.

Express the following sequences in terms of A(x), and it should not contain a summation symbol or an infinite sum:
c) a0, 0, a2, 0 , a4, 0, a6.........
d) a0, 2a1, 4a2, 8a3, 16a4........

I have thought so hard but still nothing come out form my mind. thanks in advance.

2. for part d), is it just A(2x) ? This is also the expression in terms of A(x), right?

3. Hello,

You are right. For (c), compute A(-x).

Bye.

4. Originally Posted by jmmjm
Hi, I am encountering this problem:

Let a0, a1, a2.... be an infinite sequence of non-negative integers and A(x) = the summation of an * x^n is the corresponding generating function.

Express the following sequences in terms of A(x), and it should not contain a summation symbol or an infinite sum:
c) a0, 0, a2, 0 , a4, 0, a6.........
d) a0, 2a1, 4a2, 8a3, 16a4........

I have thought so hard but still nothing come out form my mind. thanks in advance.
Do you mean $A(x)=\bigg(\sum\limits_{i=0}^{n}a_{i}\bigg)x^{n}$?

5. Hello,

No, I replied thinking that jmmjm meant $A(x)=\sum_{n=0}^{\infty}a_nx^n$.

Bye.