Answer
$2,001,000$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
\displaystyle\sum_{k=1}^{2000} k
,$ 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 $n=
2000
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{n(n+1)}{2}
\\\\=
\dfrac{2000(2000+1)}{2}
\\\\=
\dfrac{2000(2001)}{2}
\\\\=
2,001,000
.\end{array}
