Please could someone advise on my solution to the following problem. Am I wording this right or could you offer a better way?
Question is to show that $S_n =O(n^3)$ where $S_n = \sum_{k=1}^n(k^2)$
Solution: $\begin{align*}S_n &= n(a_1 + a_n)/ 2 \quad\leftarrow \text{sum of series} \\ &= n(1 + n^2)/2 \\ &= n/2 + n^3/2\end{align*}$
Since $n^3$ is the dominant term the Big-O estimate is $O(n^3)$
Should this be worded differently?
cheers