Problem: What is the value of 1+3+5+...+2017+2019−2−4−6−...2016−2018?1+3+5+...+2017+2019-2-4-6-...2016-2018?1+3+5+...+2017+2019−2−4−6−...2016−2018?
Answer Choices:
A. −1010-1010−1010 B. −1009-1009−1009 C. 100810081008 D. 100910091009 E. 101010101010
Solution:
The Expression can be written as
1+(3−2)+(5−4)+(7−6)+...+(2019−2018)=1+20182=10101 + (3 - 2) + (5 - 4) + (7 - 6) +... + (2019 - 2018) = 1 + \dfrac{2018}{2} = 10101+(3−2)+(5−4)+(7−6)+...+(2019−2018)=1+22018=1010.
Answer: E\boxed{E}E.