What is the value of $4 \cdot (-1+2-3+4-5+6-7+\cdots+1000)$?
$\textbf{(A)}\ -10 \qquad \textbf{(B)}\ 0 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 500 \qquad \textbf{(E)}\ 2000$
We group the addends inside the parentheses two at a time: 
\begin{align*} -1 + 2 - 3 + 4 - 5 + 6 - 7 + \ldots + 1000 &= (-1 + 2) + (-3 + 4) + (-5 + 6) + \ldots + (-999 + 1000) \\ &= \underbrace{1+1+1+\ldots + 1}_{\text{500 1's}} \\ &= 500. \end{align*}
Then the desired answer is $4 \times 500 = \boxed{\textbf{(E)}\ 2000}$.