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What is (-1)*(-1)^2*(-1)^3* *…*(-1)^{2019}?

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What is (-1)*(-1)^2*(-1)^3* *…*(-1)^{2019}?

by Max@Math Revolution » Thu Oct 24, 2019 11:49 pm

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[GMAT math practice question]

What is (-1)*(-1)^2*(-1)^3* *...*(-1)^{2019}?

A. -2
B. -1
C. 0
D. 1
E. 2
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by [email protected] » Fri Oct 25, 2019 5:10 am
it's an easy one when you can really see what's being asked.
We have to ignore the numbers after the first number until the second last number.
Why?
Because for every even power of -1, there's an odd power, too.
Just look at the first number -1 and last -1 (raised to an odd power) = -1
-1*-1 = 1
answer D
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by Max@Math Revolution » Sun Oct 27, 2019 6:29 pm
=>

Remember that 1 + 2 + 3 + ... + n = n(n+1)/2.
Since 1 + 2 + 3 + ... + 2019 = 2019*2020/2 = 2019*1010 and it is an even number, (-1)*(-1)^2*(-1)^3* *...*(-1)^{2019} = (-1)^{2019*1010} = 1

Therefore, D is the answer.
Answer: D
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