1. Find the sum of the numbers $1-2+3-4+5-6+\ldots+2013-2014$ and $1+2-3+4-5+6-\ldots-2013+2014$.
1. Answer: 2.

Notice that for each term of the first sum, except for 1, there is an opposite term in the second sum. The sum of opposite numbers is 0. Therefore, the total sum is $1+1=2$.

Grading criteria:

Correct answer with proper justification: 7 points.

Incorrect answer with the right idea in the justification: 2 points. Correct answer only: 1 point.