Value of Sum

What is the value of the following sum?
2006[(-1)^1+(-1)^2+(-1)^3+(-1)^4+\cdots+(-1)^{2006}]
Source: NCTM Mathematics Teacher, September 2006

Solution
The square bracket in the sum expression contains 1003 pairs of consecutive powers (-1)^n+(-1)^{n+1} which pairwise sum to zero
(-1)^1+(-1)^2=-1+1=0
(-1)^3+(1-)^4=-1+1=0
(-1)^5+(-1)^6=-1+1=0
\cdots
(-1)^{2005}+(-1)^{2006}=-1+1=0
2006[(-1)^1+(-1)^2+(-1)^3+\cdots+(-1)^{2006}]=2006[0+0+0+\cdots+0]=0

Answer: 0

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About mvtrinh

Retired high school math teacher.
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