Problem:
1−2+3−4+⋯−98+99=
Answer Choices:
A. −50
B. −49
C. 0
D. 49
E. 50
Solution:
Pairing the first two terms, the next two terms, etc. yields
1−2+3−4+⋯−98+99=(1−2)+(3−4)+⋯+(97−98)+99=−1−1−1−⋯−1+99=50
since there are 49 of the −1's
OR
1−2+3−4+⋯−98+99=1+[(−2+3)+(−4+5)+⋯+(−98+99)]=1+[1+1+⋯+1]=1+49=50.