Answer
$176$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=3}^6 (2i^2+1)
,$ substitute $
i
$ with the values from $
3
$ to $
6
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $
i
$ with the numbers from $
3
$ to $
6
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
(2(3)^2+1)+(2(4)^2+1)+(2(5)^2+1)+(2(6)^2+1)
\\\\=
(2(9)+1)+(2(16)+1)+(2(25)+1)+(2(36)+1)
\\\\=
(18+1)+(32+1)+(50+1)+(72+1)
\\\\=
19+33+51+73
\\\\=
176
.\end{array}
