Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

For every integer k from 1 to 10, inclusive, the kth term of a certain [#permalink]

Show Tags

31 Jan 2012, 17:58

6

This post received KUDOS

31

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

64% (01:42) correct
36% (01:00) wrong based on 216 sessions

HideShow timer Statistics

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

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 1) greater than 2 2)between 1 & 2 3) between 0.5 and 1 4)between 0.25 and 0.5 5)less than 0.25

Could someone please provide a solution to this problem ?

To get a hang of what the question is asking, put values for k right away. Say, k = 1, k = 2 etc You get terms such as (1/2) when k = 1, (-1/4) when k = 2 etc

T = 1/2 - 1/4 + 1/8 - 1/16 +.... + 1/512 - 1/1024 (Sum of first 10 terms)

Of course GMAT doesn't expect us to calculate but figure out the answer using some shrewdness.

We have 10 terms. If we couple them up, two terms each, we get 5 groups: T = (1/2 - 1/4) + (1/8 - 1/16) ...+ (1/512 - 1/1024)

Tell me, can we say that each group is positive? From a larger number, you are subtracting a smaller number in each bracket. e.g. 1/2 is larger than 1/4 so 1/2 - 1/4 = 1/4 i.e. a positive number 1/8 - 1/16 = 1/16, again a positive number.

We will get something similar to this: T = 1/4 + 1/16 +.... (all positives) Definitely this sum, T, is greater than 1/4 i.e. 0.25

Now, let's group them in another way.

T = 1/2 + (- 1/4 + 1/8) + (- 1/16 + 1/32) ... - 1/1024 You will be able to make 4 groups since you left the first term out. The last term will also be left out. Each bracket will give you a negative term -1/4 + 1/8 = -1/8 etc Since the first term is 1/2 i.e. 0.5, we can say that the sum T will be less than 0.5 since all the other terms are negative.

So the sum, T, must be more than 0.25 but less than 0.5

Re: For every integer k from 1 to 10, inclusive, the kth term of a certain [#permalink]

Show Tags

13 Feb 2012, 07:30

VeritasPrepKarishma wrote:

gpkk 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). If T is the sum of the first 10 terms in the sequence then T is 1) greater than 2 2)between 1 & 2 3) between 0.5 and 1 4)between 0.25 and 0.5 5)less than 0.25

Could someone please provide a solution to this problem ?

To get a hang of what the question is asking, put values for k right away. Say, k = 1, k = 2 etc You get terms such as (1/2) when k = 1, (-1/4) when k = 2 etc

T = 1/2 - 1/4 + 1/8 - 1/16 +.... + 1/512 - 1/1024 (Sum of first 10 terms)

Of course GMAT doesn't expect us to calculate but figure out the answer using some shrewdness.

We have 10 terms. If we couple them up, two terms each, we get 5 groups: T = (1/2 - 1/4) + (1/8 - 1/16) ...+ (1/512 - 1/1024)

Tell me, can we say that each group is positive? From a larger number, you are subtracting a smaller number in each bracket. e.g. 1/2 is larger than 1/4 so 1/2 - 1/4 = 1/4 i.e. a positive number 1/8 - 1/16 = 1/16, again a positive number.

We will get something similar to this: T = 1/4 + 1/16 +.... (all positives) Definitely this sum, T, is greater than 1/4 i.e. 0.25

Now, let's group them in another way.

T = 1/2 + (- 1/4 + 1/8) + (- 1/16 + 1/32) ... - 1/1024 You will be able to make 4 groups since you left the first term out. The last term will also be left out. Each bracket will give you a negative term -1/4 + 1/8 = -1/8 etc Since the first term is 1/2 i.e. 0.5, we can say that the sum T will be less than 0.5 since all the other terms are negative.

So the sum, T, must be more than 0.25 but less than 0.5

Re: For every integer k from 1 to 10, inclusive, the kth term of a certain [#permalink]

Show Tags

15 Jan 2013, 07:16

19

This post received KUDOS

3

This post was BOOKMARKED

an alternative: The series can be written as \(1/2 - 1/4 + 1/8 - 1/16.............1/1024\) Since the terms beyond \(1/16\) are too small, so I am not considering those terms. Now on adding \(1/2 - 1/4 +1/8 - 1/16\), we get \(5/16\) which is slightly more than \(4/16\). Hence its value would be around `\(0.3\).

The answer choice which includes this number is D.
_________________

Re: For every integer k from 1 to 10, inclusive, the kth term of a certain [#permalink]

Show Tags

30 Jun 2014, 19:37

Marcab wrote:

an alternative: The series can be written as \(1/2 - 1/4 + 1/8 - 1/16.............1/1024\) Since the terms beyond \(1/16\) are too small, so I am not considering those terms. Now on adding \(1/2 - 1/4 +1/8 - 1/16\), we get \(5/16\) which is slightly more than \(4/16\). Hence its value would be around `\(0.3\).

The answer choice which includes this number is D.

an alternative: The series can be written as \(1/2 - 1/4 + 1/8 - 1/16.............1/1024\) Since the terms beyond \(1/16\) are too small, so I am not considering those terms. Now on adding \(1/2 - 1/4 +1/8 - 1/16\), we get \(5/16\) which is slightly more than \(4/16\). Hence its value would be around `\(0.3\).

The answer choice which includes this number is D.

QUESTION : WHERE IS 1/1024 coming from?

When you put k = 10 (to get the last term) in the given expression \((-1)^{k+1}*(1/2^k)\), you get -1/1024
_________________

This question comes up every so often in this Forum. There are a couple of different ways of thinking about this problem, but they all require a certain degree of "math."

Without too much effort, you can deduce what the sequence is:

+1/2, -1/4, +1/8, -1/16, etc.

The "key" to solving this question quickly is to think about the terms in "sets of 2"…

1/2 - 1/4 = 1/4

Since the first term in each "set of 2" is greater than the second (negative) term, we now know that each set of 2 will be positive.

1/8 - 1/16 = 1/16

Now we know that each additional set of 2 will be significantly smaller than the prior set of 2.

1/4....1/16....1/64....etc.

Without doing all of the calculations, we know…. We have 1/4 and we'll be adding tinier and tinier fractions to it. Since there are only 10 terms in the sequence, there are only 5 sets of 2, so we won't be adding much to 1/4. Based on the answer choices, only one answer makes any sense…

Re: For every integer k from 1 to 10, inclusive, the kth term of a certain [#permalink]

Show Tags

16 Jun 2016, 21:01

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

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

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...