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Algebra Difficulty 1.9 Junior Find the answer

What is (−1)1+(−1)2+...+(−1)2006(-1)^{1} + (-1)^{2} + ... + (-1)^{2006} ?

Pick one

Solution

Since −1-1 raised to an odd integer is −1-1 and −1-1 raised to an even integer exponent is 11:
(−1)1+(−1)2+...+(−1)2006=(−1)+(1)+...+(−1)+(1)=(C) 0.(-1)^{1} + (-1)^{2} + ... + (-1)^{2006} = (-1) + (1) + ... + (-1)+(1) = \boxed{\textbf{(C) }0}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.