I have the equation $T(n) = T(n-2) + n^5 + n$ for $n\ge2$.
I want to write $n$ in the form of $bk+r$. Thus $n=2k+r$ where $0\le r<2$, i.e. $r=0$ or $r=1$.
I have come to the conclusion that $T(n)$ follows the following formula:
$\begin{align*}T(n) = T(r) &+ [(2+r)^5 + (2+r)] + [(2\cdot2+r)^5 + (2\cdot2+r)] + \ldots \\ &+ [(2i+r)^5 + (2i+r)] + \ldots + [(2k+r)^5 + (2k+r)]\end{align*}$
However, I cannot tell determine what the rate of growth, i.e. the order of the function is, in terms of $n$. This is problem 5 in the pdf here.
That pdf also contains the formulas I've used to get thus far. Any help would be awesome. I can't seem to figure this out.