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

## Problem 5

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

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

## Solution

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

## Alternate Solution

We can rewrite the given expression as $1+(3-2)+(5-4)+\cdots +(2017-2016)+(2019-2018)=1+1+1+\cdots+1$. The number of $1$s is the same as the number of terms in $1,3,5,7\dots ,2017,2019$. Thus the answer is $\boxed{\textbf{(E) }1010}$