Answer
$35$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^5 (2i+1)
,$ substitute $i$ with the values from $
1
$ to $
5
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $i$ with the numbers from $
1
$ to $
5
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
(2(1)+1)+(2(2)+1)+(2(3)+1)+(2(4)+1)+(2(5)+1)
\\\\=
(2+1)+(4+1)+(6+1)+(8+1)+(10+1)
\\\\=
3+5+7+9+11
\\\\=
35
.\end{array}
