Answer
$$70$$
Work Step by Step
$$\eqalign{
& \sum\limits_{i = 1}^5 {\left( {{i^2} + i} \right)} \cr
& {\text{Evaluate }}i = 1{\text{ to }}i = 5 \cr
& i = 1 \cr
& = {\left( 1 \right)^2} + \left( 1 \right) = 2 \cr
& i = 2 \cr
& = {\left( 2 \right)^2} + \left( 1 \right) = 6 \cr
& i = 3 \cr
& = {\left( 3 \right)^2} + \left( 1 \right) = 12 \cr
& i = 4 \cr
& = {\left( 4 \right)^2} + \left( 1 \right) = 20 \cr
& i = 5 \cr
& = {\left( 5 \right)^2} + \left( 1 \right) = 30 \cr
& {\text{The sum is}} \cr
& \sum\limits_{i = 1}^5 {\left( {{i^2} + i} \right)} = 2 + 6 + 12 + 20 + 30 \cr
& \sum\limits_{i = 1}^5 {\left( {{i^2} + i} \right)} = 70 \cr} $$
