# Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises - Page 646: 60

$2,001,000$

#### 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}

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