Problem:
Find the value of the expression
100−98+96−94+92−90+⋯+8−6+4−2.
Answer Choices:
A. 20
B. 40
C. 50
D. 80
E. 100
Solution:
Evaluate the expression by grouping as follows:
(100−98)+(96−94)+⋯+(8−6)+(4−2)=2+2+⋯+2+2=2⋅25=50.
Answer: C.
The problems on this page are the property of the MAA's American Mathematics Competitions