Answer
$28$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=-1}^5 (i^2-2i)
,$ 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}
((-1)^2-2(-1))+(0^2-2(0))+(1^2-2(1))+(2^2-2(2))+(3^2-2(3))+(4^2-2(4))+(5^2-2(5))
\\\\=
(1+2)+(0-0)+(1-2)+(4-4)+(9-6)+(16-8)+(25-10)
\\\\=
3+0-1+0+3+8+15
\\\\=
28
.\end{array}
