Answer
$426$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^4 \dfrac{x_i^3+1000}{x_i+10}
,$ substitute $
i
$ with the values from $
1
$ to $
4
.$ Then substitute the given values for each $x_i$'s
$\bf{\text{Solution Details:}}$
Substituting $
i
$ with the numbers from $
1
$ to $
4
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{x_1^3+1000}{x_1+10}+\dfrac{x_2^3+1000}{x_2+10}+\dfrac{x_3^3+1000}{x_3+10}+\dfrac{x_4^3+1000}{x_4+10}
.\end{array}
Using the given values $x_1=-2, x_2=-1, x_3=0,$ and $x_4=1,$ the expression above evaluates to
\begin{array}{l}\require{cancel}
\dfrac{(-2)^3+1000}{-2+10}+\dfrac{(-1)^3+1000}{-1+10}+\dfrac{0^3+1000}{0+10}+\dfrac{1^3+1000}{1+10}
\\\\=
\dfrac{-8+1000}{8}+\dfrac{-1+1000}{9}+\dfrac{0+1000}{10}+\dfrac{1+1000}{11}
\\\\=
\dfrac{992}{8}+\dfrac{999}{9}+\dfrac{1000}{10}+\dfrac{1001}{11}
\\\\=
124+111+100+91
\\\\=
426
.\end{array}
