For every integer K?... HELP

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For every integer K?... HELP

by gmatpup » Sat Dec 24, 2011 9:23 am
Please help! Thank you!!

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). If T is the sum of the first 10 terms, then T is?

A. greater than 2
B. between 1 and 2
C. between 1/2 and 2
D. between 1/4 and 1/2
E. less than 1/4


Answer is D
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by pemdas » Sat Dec 24, 2011 1:43 pm
very useful question

we can solve this question two ways: by applying number property knowledge or applying algebra (sequence theory)

first simplify to get the sequence 1/2 -1/4 +1/8 -1/16 ... -1/2^10 and decide about the interval

the second method, algebra (geometric sequence) b(1)=1/2, q=(-1/2), n=10
1/2 * (1-1/2^10)/(1+1/2)

I would use algebra here and see right away that (1-1/2^10) in the numerator is approx. ~1, hence 1/2 *1/(1+1/2) OR 1/2 *2/3 = 1/3

it's evident answer is D
gmatpup wrote:Please help! Thank you!!

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). If T is the sum of the first 10 terms, then T is?

A. greater than 2
B. between 1 and 2
C. between 1/2 and 2
D. between 1/4 and 1/2
E. less than 1/4


Answer is D
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