Answer
$\dfrac{75}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=-1}^2 5(2)^i
,$ substitute $
i
$ with the values from $
-1
$ to $
2
$ and then simplify the expression.
$\bf{\text{Solution Details:}}$
Substituting $
i
$ with the numbers from $
-1
$ to $
2
,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
5(2)^{-1}+5(2)^0+5(2)^1+5(2)^2
\\\\=
\dfrac{5}{2^1}+5(1)+5(2)+5(4)
\\\\=
\dfrac{5}{2}+5+10+20
\\\\=
\dfrac{5}{2}+35
\\\\=
\dfrac{5}{2}+\dfrac{70}{2}
\\\\=
\dfrac{75}{2}
.\end{array}
