Difference between revisions of "2018 AMC 8 Problems/Problem 5"

Revision as of 12:50, 21 November 2018

What is the value of $1+3+5+\cdots+2017+2019-2-4-6-\cdots-2016-2018$ ?

Rearranging the terms, we get $(1-2)+(3-4)+(5-6)+...(2017-2018)+2019$ , and our answer is $-1009+2019=\boxed{1010}, \textbf{(E)}$

$\textbf{(A) }-1010\qquad\textbf{(B) }-1009\qquad\textbf{(C) }1008\qquad\textbf{(D) }1009\qquad \textbf{(E) }1010$

2018 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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 ==Problem 5==
 What is the value of <math>1+3+5+\cdots+2017+2019-2-4-6-\cdots-2016-2018</math>?
+==Solution==
+Rearranging the terms, we get <math>(1-2)+(3-4)+(5-6)+...(2017-2018)+2019</math>, and our answer is <math>-1009+2019=\boxed{1010}, \textbf{(E)}</math>
 <math>\textbf{(A) }-1010\qquad\textbf{(B) }-1009\qquad\textbf{(C) }1008\qquad\textbf{(D) }1009\qquad \textbf{(E) }1010</math>
 {{AMC8 box|year=2018|num-b=4|num-a=6}}