I'm using the iteration method to find the complexity of the following recurrence (I can't use the master theorem because it doesn't match the MT form).
$$ T(n) = T(n-10) + \sqrt{n} \text{ and } T(1) = 1 $$
Assuming my solution is correct, I have
$$T(n) = T(n-10i) + \sum_{j=0}^{i-1} \sqrt{n-10j} $$
that means
$$T(1) = 1 \text{ when } i = \frac{n-1}{10}$$
hence
$$T(N) = T(1) + \sum_{j=0}^{\frac{n-1}{10}} \sqrt{n-10j}$$
At this point I'm stuck. I'm not sure if I can simplify the sum by removing constants. My final result is something like $\Theta(n * \sqrt{n})$, but I definitely don't trust my result.