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# For every integer K from 1 to 10 inclusive, the Kth term of

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Manager
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For every integer K from 1 to 10 inclusive, the Kth term of [#permalink]  30 Dec 2006, 20:16
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For every integer K from 1 to 10 inclusive, the Kth term of a certain sequence is given by (-1)^k+1 * (1/2^k).

(that is negative one to the k+1 power ....times 1 over 2 to the kth power)

If T is the sum of the first ten terms in 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
Senior Manager
Joined: 05 Oct 2006
Posts: 267
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Re: GMAT Prep PS [#permalink]  30 Dec 2006, 20:31
a1 = 1/2
a2 = -(1/2)^2
a3 = 1/2 ^3

hence it is a geometric progression whose common ratio is r = -1/2

hence T = a1 * ( r^(n+1) - 1 )/(r - 1)
= 1/3 ( 1 + 1/2 ^ 11)
= approx 1/3 * 1= 0.33

hence choice d
Senior Manager
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Re: GMAT Prep PS [#permalink]  30 Dec 2006, 23:37
ellisje22 wrote:
For every integer K from 1 to 10 inclusive, the Kth term of a certain sequence is given by (-1)^k+1 * (1/2^k).

(that is negative one to the k+1 power ....times 1 over 2 to the kth power)

If T is the sum of the first ten terms in 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

T = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + 1/128 - 1/256 + 1/512 - 1/1024.

T = 1/4 + 1/16 + 1/64 + 1/256 + 1/1024.

By simple inspection you notice the 4 last terms are less than 1/4; then T is between 1/4 and 1/2. D.
Re: GMAT Prep PS   [#permalink] 30 Dec 2006, 23:37
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