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

Source: 2018 AMC 8 #5

November 20, 2018
AMC 82018 AMC 8

Problem Statement

What is the value of 1+3+5+⋯+2017+2019−2−4−6−⋯−2016−20181+3+5+\cdots+2017+2019-2-4-6-\cdots-2016-2018?
<spanclass=′latex−bold′>(A)</span>−1010<spanclass=′latex−bold′>(B)</span>−1009<spanclass=′latex−bold′>(C)</span>1008<spanclass=′latex−bold′>(D)</span>1009<spanclass=′latex−bold′>(E)</span>1010<span class='latex-bold'>(A) </span>-1010\qquad<span class='latex-bold'>(B) </span>-1009\qquad<span class='latex-bold'>(C) </span>1008\qquad<span class='latex-bold'>(D) </span>1009\qquad <span class='latex-bold'>(E) </span>1010
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