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If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 =

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If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink] New post   Updated on: 23 Oct 2013, 01:19
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If \(x =\frac{1}{2}\), then \(x^{-1} + x^{-2} + x^{-3} + x^{-4} =\)

(A) 1/32
(B) 15/16
(C) 1
(D) 30
(E) 32
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D

Originally posted by avohden on 22 Oct 2013, 19:40.
Last edited by Bunuel on 23 Oct 2013, 01:19, edited 1 time in total.
Edited the question.
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Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink] New post   23 Oct 2013, 01:20
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avohden wrote:
If \(x =\frac{1}{2}\), then \(x^{-1} + x^{-2} + x^{-3} + x^{-4} =\)

(A) 1/32
(B) 15/16
(C) 1
(D) 30
(E) 32



\(x^{-1} + x^{-2} + x^{-3} + x^{-4} =\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}=2+4+8+16=30\).

Answer: D.
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Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink] New post   23 Oct 2013, 07:55
Official Explanation

Answer: D --- Plug in 1/2 for each of the occurrences of x:

x^-1 + x^-2 + x^-3 + x^-4 =
(1/2)^-1 + (1/2)^-2 + (1/2)^-3 + (1/2)^-4 =
1/(1/2) + 1/(1/2)^2 + 1/(1/2)^3 + 1/(1/2)^4 =
2 + 1/(1/4) + 1/(1/8) + 1/(1/16) =
2 + 4 + 8 + 16 =
30, choice (D).
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Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink] New post   26 Feb 2014, 02:46
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Did in this way

Given x = 1/2, so 1/x = 2

Placing the values, 2+4+8+16 = 30 = Answer = D
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Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink] New post   20 Jan 2021, 10:31
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Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink]
20 Jan 2021, 10:31
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