Video solution:

Click to load, then click again to play

Written solution:

Group the terms in blocks of four: $(1+2+3-4)+(5+6+7-8)+\cdots+(197+198+199-200)$. The $j$th block is $(4j-3)+(4j-2)+(4j-1)-4j=8j-6$.

There are $50$ blocks, so the sum is $\sum_{j=1}^{50}(8j-6)=8\cdot\dfrac{50\cdot51}{2}-6\cdot50=9900$. Thus, B is the correct answer.