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n is a positive integer. What is the value of (-1)n+2 – (-

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n is a positive integer. What is the value of (-1)n+2 – (-

by Max@Math Revolution » Wed Sep 18, 2019 11:57 pm

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[GMAT math practice question]

n is a positive integer. What is the value of (-1)^{n+2} - (-1)^{n-1} +(-1)^{n+1} -(-1)^n

A. -3
B. -2
C. -1
D. 0
E. 1
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by Max@Math Revolution » Sun Sep 22, 2019 5:38 pm
=>

If n is an odd integer, then (-1)^{n+2} - (-1)^{n-1} +(-1)^{n+1} -(-1)^n = (-1) - 1 + 1 - (-1) = 0.

If n is an even integer, then (-1)^{n+2} - (-1)^{n-1} +(-1)^{n+1} -(-1)^n = 1 - (-1) + (-1) - 1 = 0.
Thus it is always 0.

Therefore, D is the answer.
Answer: D
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