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For every integer k from 1 to 10, inclusive, the kth term of [#permalink]
14 Nov 2006, 15:55

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

40% (02:26) correct
60% (01:35) wrong based on 50 sessions

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 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

Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]
14 Nov 2006, 17:16

Q. 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 in the sequence, then T is

a) > 2
b) between 1 and 2
c) between 1/2 and 1
d) between 1/4 and 1/2
e) less then 1/4

Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]
14 Nov 2006, 17:30

I got D for this one. I used the same logic as Damager did. However, I think since the sequence alters a positive and a negative, ie the first term is 1/2, the second is -1/4, the third is 1/8, fourth is -1/16. So even with the first two terms, the sum should be 1/4 and then adding smaller and smaller amount as the sequence goes. So Asn D between 1/4 and 1/2

Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]
15 Nov 2006, 00:48

enola wrote:

I got D for this one. I used the same logic as Damager did. However, I think since the sequence alters a positive and a negative, ie the first term is 1/2, the second is -1/4, the third is 1/8, fourth is -1/16. So even with the first two terms, the sum should be 1/4 and then adding smaller and smaller amount as the sequence goes. So Asn D between 1/4 and 1/2

So adding smaller and smaller amounts makes it go to 1/2 even though the terms are positive and negative. Can you please explain a bit more about your logic?

Q. 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 in the sequence, then T is

a) > 2
b) between 1 and 2
c) between 1/2 and 1
d) between 1/4 and 1/2
e) less then 1/4

since you are summing, the number is going to slowly move between 1/4 and 1/2 but staying above 1/4 and below 1/2. It keeps moving by smaller and smaller fractions, but it always will be above 1/4 and under 1/2. Look at it this way. The first two numbers establish the range. It starts at a 1/2 then drops to 1/4 and each time it lowers and raises by a smaller increment. What you will have is something that looks like this:

meaning, first the number swings a lot, then it slowly swings by increasingly an infinitely smaller increments. Eventually you are adding 1/10000000 and then subtracting 1/100000000 and so on into infinity.

Long story short, you have the number .5 and .25. The number made by this sum will just keep getting more and more decimal places instead of moving past one of those two numbers.

I really hope this long ass explanation is right or it will look pretty stupid .

I'm sitting in Norway and its almost 1am, so who knows.

Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]
26 Jul 2014, 10:39

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