2013 AMC8 Problem 3

#1
What is the value of \(4 \cdot (-1+2-3+4-5+6-7+\cdots+1000)\)?

\(\textbf{(A)}\ -10 \qquad \textbf{(B)}\ 0 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 500 \qquad \textbf{(E)}\ 2000\)