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For any integer k from 1 to 10, inclusive, the kth of a

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Senior Manager
Joined: 07 Jan 2008
Posts: 384
For any integer k from 1 to 10, inclusive, the kth of a [#permalink]

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24 Aug 2008, 13:52
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For any integer k from 1 to 10, inclusive, the kth of a certain sequence is given by [(-1)^(k+1)]*(1 / 2^k). If T is the sum of the first 10 terms of the sequence, then T is:
A. greater than 2
B. between 1 and 2
C. between 1/2 and 1
D. between 1/4 and 1/2
E. less than 1/4

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Intern
Joined: 20 Aug 2008
Posts: 27

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24 Aug 2008, 14:05
The answer should be D:between 1/4 and 1/2.

For every odd and even term you will get a positive value which is half the even term. As the series moves on for every alternate even term that also halves.

say 1 and 2 would be 1/2 and -1/4 resulting to 1/4.
similarly 3 and 4 would be 1/8 and -1/16 resulting to 1/8.

This goes on.

When add each term you will get an answer which is close to < 0.5

Regards,
Max
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Joined: 07 Nov 2007
Posts: 1761
Location: New York

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24 Aug 2008, 15:04
lexis wrote:
For any integer k from 1 to 10, inclusive, the kth of a certain sequence is given by [(-1)^(k+1)]*(1 / 2^k). If T is the sum of the first 10 terms of the sequence, then T is:
A. greater than 2
B. between 1 and 2
C. between 1/2 and 1
D. between 1/4 and 1/2
E. less than 1/4

expand the series
$$S=[1/2-1/2^2] +[1/2^3-1/2^4]+..$$
$$= 1/4+1/2^2*1/4+1/2^4*1/4+..$$
$$= 1/4 (1+ 1/2^2+1/2^4+1/2^6+1/2^8+1/2^10)$$

Highligthed red part is 1/4 <1/2

D

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: PS: Set   [#permalink] 24 Aug 2008, 15:04
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