Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 28 May 2016, 13:53

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For every integer k from 1 to 10 inclusive the kth terem of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 17 Sep 2011
Posts: 209
Followers: 0

Kudos [?]: 82 [3] , given: 8

For every integer k from 1 to 10 inclusive the kth terem of [#permalink]

### Show Tags

31 Jan 2012, 17:58
3
KUDOS
23
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 29 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
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 ?
_________________

_________________
Giving +1 kudos is a better way of saying 'Thank You'.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6578
Location: Pune, India
Followers: 1794

Kudos [?]: 10785 [33] , given: 211

Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink]

### Show Tags

01 Feb 2012, 23:11
33
KUDOS
Expert's post
14
This post was
BOOKMARKED
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

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 27 Jul 2010 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 1 Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink] ### Show Tags 11 Feb 2012, 18:44 Perfect explanation! Thanks Karishma! Intern Joined: 01 Dec 2010 Posts: 3 Followers: 0 Kudos [?]: 0 [0], given: 34 Re: For every integer k from 1 to 10 inclusive the kth terem of [#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 Answer (D) VP Status: Been a long time guys... Joined: 03 Feb 2011 Posts: 1420 Location: United States (NY) Concentration: Finance, Marketing GPA: 3.75 Followers: 165 Kudos [?]: 1067 [15] , given: 62 Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink] ### Show Tags 15 Jan 2013, 07:16 15 This post received KUDOS Expert's post 2 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. _________________ Intern Joined: 21 Dec 2011 Posts: 14 Schools: Tepper '17 (S) Followers: 0 Kudos [?]: 10 [4] , given: 7 Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink] ### Show Tags 24 Feb 2014, 18:23 4 This post received KUDOS I did it the following way. K=(1/2)-(1/4)+(1/8)-(1/16)+..... ----- 1 Multiply K by 2 2K=1-(1/2)+(1/4)-.....-(1/512) ------- 2 Adding 1 and 2 3K = 1 -(1/1024) K= (1/3) -{1/(3*1024)} Now 1/(3*1024) will be very small So K= 1/3 = .3333 Ans Option D Manager Joined: 28 Dec 2013 Posts: 79 Followers: 0 Kudos [?]: 1 [0], given: 3 Re: For every integer k from 1 to 10 inclusive the kth terem of [#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. QUESTION : WHERE IS 1/1024 coming from? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6578 Location: Pune, India Followers: 1794 Kudos [?]: 10785 [0], given: 211 Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink] ### Show Tags 30 Jun 2014, 19:47 Expert's post 1 This post was BOOKMARKED sagnik242 wrote: 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. 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Current Student
Joined: 03 Feb 2013
Posts: 929
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Followers: 99

Kudos [?]: 648 [4] , given: 546

Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink]

### Show Tags

12 Jul 2014, 07:54
4
KUDOS
This is GP.

The terms will be 1/2-1/4+1/8-....

Common ratio is (-1/4)/(1/2) = -1/2

So the sum of terms = 1/2 [1- (-1/2)^10]/(1-(-1/2)) = 1/2 *[1-1/1024]/3/2 = 1023/(1024*3) close to 1/3 so Option D
_________________

Thanks,
Kinjal
Struggling with GMAT ? Experience http://www.gmatify.com/

My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961

Please click on Kudos, if you think the post is helpful

Intern
Joined: 16 Jan 2012
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink]

### Show Tags

17 Jul 2014, 22:03
Can we some how solve this question using sum of a series formula- S = (n/2) × (2a + (n-1)d)??
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6578
Location: Pune, India
Followers: 1794

Kudos [?]: 10785 [0], given: 211

Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink]

### Show Tags

17 Jul 2014, 22:14
Expert's post
sumitaries wrote:
Can we some how solve this question using sum of a series formula- S = (n/2) × (2a + (n-1)d)??

The formula you are talking about is used for sum of terms of an Arithmetic Progression only.

Read about it here: http://www.veritasprep.com/blog/2012/03 ... gressions/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 24 Feb 2014 Posts: 6 Schools: ISB Followers: 0 Kudos [?]: 1 [0], given: 21 Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink] ### Show Tags 04 Aug 2014, 06:45 1 This post was BOOKMARKED http://tinypic.com/r/2lvk4z5/8 Please check a simpler solution to the above problem in the above image link. Cheers. Manager Joined: 18 Jul 2013 Posts: 54 Followers: 0 Kudos [?]: 4 [0], given: 151 For every integer k from 1 to 10 inclusive the kth terem of [#permalink] ### Show Tags 07 Oct 2014, 15:19 1 This post was BOOKMARKED Rohitesh, Where did u get this 1/6? Intern Joined: 08 Dec 2014 Posts: 5 Followers: 0 Kudos [?]: 0 [0], given: 2 Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink] ### Show Tags 13 Dec 2014, 21:00 taleesh wrote: Rohitesh, Where did u get this 1/6? He used the summation of geometric series (base 1/4), I think. Beautiful solution. Intern Joined: 16 Jan 2015 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 18 Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink] ### Show Tags 03 Jun 2015, 13:56 I used the same calculation as above, which will probably take little more than 2 minutes. Is there a simple version to solve this problem? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 6417 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 270 Kudos [?]: 1896 [1] , given: 161 Re: For every integer k from 1 to 10 inclusive the kth terem of [#permalink] ### Show Tags 03 Jun 2015, 15:14 1 This post received KUDOS Expert's post Hi vijaydoli, 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… Final Answer: [Reveal] Spoiler: D GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: For every integer k from 1 to 10 inclusive the kth terem of   [#permalink] 03 Jun 2015, 15:14
Similar topics Replies Last post
Similar
Topics:
169 For every integer k from 1 to 10, inclusive, the kth term of 40 07 Jan 2010, 06:22
for every integer k from 1-10 inclusive, the kth term of a 10 30 Oct 2007, 20:14
For every integer k from 1 to 10, inclusive, the kth term of a certain 8 11 Aug 2007, 13:14
2 For every integer k from 1 to 10, inclusive, the kth term of 7 03 Jun 2007, 03:27
9 For every integer k from 1 to 10, inclusive, the kth term of 11 14 Nov 2006, 16:55
Display posts from previous: Sort by

# For every integer k from 1 to 10 inclusive the kth terem of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.