Let $S = \displaystyle{}\sum_{k=1}^{n}(1 + 2 + \dots + k)$
$\Rightarrow S = \displaystyle{}\sum_{k=1}^{n}\left( \frac{k(k+1)}{2}\right)$
$\Rightarrow S = \displaystyle{}\sum_{k=1}^{n}\left( \frac{k^{2}+k}{2}\right)$
$\Rightarrow S = \displaystyle{}\frac{1}{2}\left [\sum_{k=1}^{n}k^{2} + \sum_{k=1}^{n}k \right]$
$\Rightarrow S = \dfrac{1}{2} \left [ (1^{2} + 2^{2} + 3^{2} + \dots + n^{2}) + (1 + 2 + 3 +\dots + n) \right]$
$\Rightarrow S = \dfrac{1}{2} \left [ \left(\dfrac{n(n+1)(2n+1)}{6}\right) + \left(\dfrac{n(n+1)}{2}\right) \right]$
Now, we can multiply the terms, and get the degree of the polynomial $ = 3.$
$\textbf{PS:}$
- $1 + 2 + 3 + \dots + n = \dfrac{n(n+1)}{2}$
- $1^{2} + 2^{2} + 3^{2} + \dots + n^{2} = \dfrac{n(n+1)(2n+1)}{6}$
