## Calculus (3rd Edition)

$$\sum_{i=1}^{n} \sqrt{i+i^{3}}$$
Given $$\sqrt{1+1^{3}}+\sqrt{2+2^{3}}+\dots+\sqrt{n+n^{3}}$$ The first term is $\sqrt{1+1^{3}}$, the last term is $\sqrt{n+n^{3}}$, and we observe that terms are increasing by $1$, so $$\sqrt{1+1^{3}}+\sqrt{2+2^{3}}+\dots+\sqrt{n+n^{3}}=\sum_{i=1}^{n} \sqrt{i+i^{3}}$$