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Which of the following is closest to (-3/4)^199?

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Which of the following is closest to (-3/4)^199?  [#permalink]

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New post 10 Sep 2016, 20:41
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Which of the following is closest to (-3/4)^199?
A. -1
B. -1/2
C. 0
D. 1
E. 2

*An answer will be posted in 2 days.

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Re: Which of the following is closest to (-3/4)^199?  [#permalink]

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New post 10 Sep 2016, 21:58
MathRevolution wrote:
Which of the following is closest to (-3/4)^199?
A. -1
B. -1/2
C. 0
D. 1
E. 2

*An answer will be posted in 2 days.



Answer is C)0
since (3/4)^4 = 81/256 and if far smaller than 1/2, this will reach very close to zero.
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Re: Which of the following is closest to (-3/4)^199?  [#permalink]

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New post 11 Sep 2016, 15:22
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MathRevolution wrote:
Which of the following is closest to (-3/4)^199?
A. -1
B. -1/2
C. 0
D. 1
E. 2

*An answer will be posted in 2 days.


Let's make a few observations and look for a pattern...

(-3/4)¹ = -3/4
(-3/4)² = (-3/4)(-3/4) = 9/16 ≈ a little more than 1/2
(-3/4)³ = (-3/4)(-3/4)(-3/4) = -27/64 ≈ a little more than -1/2
(-3/4)⁴ = (-3/4)(-3/4)(-3/4)(-3/4) = 81/256 ≈ a little less than 1/3

As the exponent, n, increases, the MAGNITUDE of (-3/4)^n decreases
That is, as the exponent, n, increases, the value of (-3/4)^n approaches zero
So, 0 is the closest value to (-3/4)^199

Answer:


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Re: Which of the following is closest to (-3/4)^199?  [#permalink]

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New post 12 Sep 2016, 07:58
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From -1<x<1, x^n approaches 0 as n increases. Hence, the correct answer is C.
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Re: Which of the following is closest to (-3/4)^199?  [#permalink]

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New post 12 Sep 2016, 16:38
MathRevolution wrote:
From -1<x<1, x^n approaches 0 as n increases. Hence, the correct answer is C.

Great question with the implication of very basic logic.
Thanks for the explanation.
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Re: Which of the following is closest to (-3/4)^199?  [#permalink]

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Re: Which of the following is closest to (-3/4)^199?   [#permalink] 20 Jan 2019, 11:52
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