Skip to main content

2006 AMC 10B Problem 1

Problem 1 of 25EasierArithmeticProblem-Solving Techniques

What is (−1)1+(−1)2+⋯+(−1)2006?(-1)^1 + (-1)^2 + \cdots + (-1)^{2006}?

Answer choices

Show solution

Solution

There are 20062006 terms. Pairing consecutive terms gives (−1+1)+(−1+1)+⋯ .(-1+1)+(-1+1)+\cdots. Since 20062006 is even, every term pairs off and the sum is 0.0. Thus, the correct answer is C.
AoPS wiki

Tagged: exponent · pairing and grouping

More practice