Problem
Let $f(x)$ be the ordinary generating function for the sequence $ \{\ a_0 , a_1, a_2,... \}\ $. Find the ordinary generating sequence for the following sequence: $$b_n = a_n + c \ \ \ , n \in \mathbb{N}_0$$
My attempt
I'm guessing $c$ is just any constant. I'm having trouble understanding the question however.
I solved these types of questions such as:
Find an ordinary generating function for $a_n = n$
I did this by writing out $a_n$ as $1+2+3+4...$ and then writing out the power series $A(x) = x + 2x^2 + 3x^3...$.
Now I could write:
$$\frac{1}{1-x} = \sum_{n=0}^\infty x^n$$
As I can see this from the power series.
From here I just had to algebraically manipulate both sides to find the generating function which I wanted to look like the power series $$\sum_{n=0}^\infty nx^n$$
However I'm having trouble relating this to my current question!
Thank you.
The generating function for $b_n$ is by definition
$$g(x)=\sum_{n=0}^\infty b_n x^n=\sum_{n=0}^\infty (a_n+c) x^n=\sum_{n=0}^\infty a_n x^n+c\sum_{n=0}^\infty x^n$$
You know each of the two functions on RHS..