All done using geometric series $\sum_{n>0} ^{\infty} x^n$
a) Find expression for the generating function of the sequence with terms $q_n=n^4$.
b) Find expression for the generating function of the sequence with terms $r_n=\sum_{k=0} ^n k^4$.
For a) I basically started with:
$\frac{1}{1-x}=1+x+x^2+\cdots$, etc.
and differentiated and multiplied by $x$ consecutively a few times to come up with the answers for a) and b) and b) was just $\frac{1}{1-x}$ times a).
But I can't help but feel my answers are wrong, so I was wondering if somebody could confirm if I was doing the right thing? I.e. multiplying by $x$ both sides, differentiate with respect to $x$, etc. etc. consecutively a few times till pattern looks like generating function of $q_n$ and $r_n$?
also, I was wondering for part c), find a polynomial expression for r_n, I have no idea how to do that, apparently by induction is incorrect, and have to use convolution or something