I've been working on my Algorithms homework and figuring out the $\mathcal{O}$, $\Omega$, $\Theta$, etc, of several algorithms. I'm proving them by finding their $c$ and $n_0$ values and all is going well.
However, I've come across my last two problems in the set and I'm struggling figuring out how to do them (and google isn't helping much).
I haven't had to figure out the $\mathcal{O}$/$\Omega$ of summations before.
My last two problems are:
- $\displaystyle\sum_{i = 2}^{n} \log i \in \Theta\left(n\log n\right)$
- $\displaystyle\sum_{i = 1}^{n} i^p \in \Theta\left(n^{p + 1}\right),\forall p\ge1$
My question is, How do I show that or how do I start thinking about this?