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2006 AMC 10B Problem 1

Problem 1 of 25EasierAlgebraCounting & Probability

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

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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.

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Concepts: exponent · pairing and grouping

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.