Answer
$-2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^4 [(-2)^i-3]
,$ substitute $
i
$ with the values from $
1
$ to $
4
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $
i
$ with the numbers from $
1
$ to $
4
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
[(-2)^1-3]+[(-2)^2-3]+[(-2)^3-3]+[(-2)^4-3]
\\\\=
[-2-3]+[4-3]+[-8-3]+[16-3]
\\\\=
-5+1-11+13
\\\\=
-2
.\end{array}
