Difference between revisions of "2006 AMC 10B Problems/Problem 1"
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== Solution == | == Solution == | ||
− | Since <math>-1</math> raised to an [[odd integer | odd]] [[exponent]] is <math>-1</math> and <math>-1</math> raised to an [[even integer]] exponent is <math>1</math>: | + | Since <math>-1</math> raised to an [[odd integer | odd]] [[exponentiation | exponent]] is <math>-1</math> and <math>-1</math> raised to an [[even integer]] exponent is <math>1</math>: |
<math> (-1)^{1} + (-1)^{2} + ... + (-1)^{2006} = (-1) + (1) + ... + (-1)+(1) = 0 \Longrightarrow C </math> | <math> (-1)^{1} + (-1)^{2} + ... + (-1)^{2006} = (-1) + (1) + ... + (-1)+(1) = 0 \Longrightarrow C </math> |
Revision as of 14:02, 9 November 2006
Problem
What is ?
Solution
Since raised to an odd exponent is
and
raised to an even integer exponent is
: