Problem:
What is the value of 1+3+5+...+2017+2019−2−4−6−...2016−2018?
Answer Choices:
A. −1010
B. −1009
C. 1008
D. 1009
E. 1010
Solution:
Rearranging the terms, notice that the expression in the question is equal to:
(1+3−2)+(5−4)+⋯+(2017−2016)+(2019−2018)
Each term is equal to 1, and there are 22019−1−1=1010 terms, so the total sum is
1010⋅1=1010.
Thus, E is the correct answer.
Answer: E.
The problems on this page are the property of the MAA's American Mathematics Competitions