Answer
$500,500$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
\displaystyle\sum_{i=1}^{1000} i
,$ use the summation properties and then simplify.
$\bf{\text{Solution Details:}}$
Using a property of the summation which is given by $\displaystyle\sum_{i=1}^n i=\dfrac{n(n+1)}{2},$ with $n=
1000
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{n(n+1)}{2}
\\\\=
\dfrac{1000(1000+1)}{2}
\\\\=
\dfrac{1000(1001)}{2}
\\\\=
500,500
.\end{array}