Given is the following recurrence relation:
$T(n)=n^2+T(\frac{n}{2})+T(\frac{n}{4})+T(\frac{n}{8})+...+T(\frac{n}{2^k})$
where $k$ is some constant and $n = 2^t$ for some $t\in \mathbb{Z}$.
I'm trying to find an asymptotic bound for $T(n)$.
My work so far:
First, I've tried to guess and prove by induction. Then, I tried to solve using a recursion tree, but I couldn't find any obvious pattern to follow.