Problem:
What is (−1)1+(−1)2+⋯+(−1)2006?
Answer Choices:
A. −2006
B. −1
C. 0
D. 1
E. 2006
Solution:
Because
(−1)k={1,−1, if k is even if k is odd
the sum can be written as
(−1+1)+(−1+1)+⋯+(−1+1)=0+0+⋯+0=(C)0
The problems on this page are the property of the MAA's American Mathematics Competitions