It is currently 20 Jul 2017, 19:52

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 term of

Author Message
TAGS:

Hide Tags

Manager
Joined: 12 Jun 2006
Posts: 55
For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

14 Nov 2006, 16:55
1
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:40) correct 39% (01:49) wrong based on 117 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

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-every-integer-k-from-1-to-10-inclusive-the-kth-term-of-88874.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Jul 2014, 11:52, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5042
Location: Singapore
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

14 Nov 2006, 17:52
(-1)^K+1 . (1/2^K). --> The dots mean multiply?
Manager
Joined: 12 Jun 2006
Posts: 55
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

14 Nov 2006, 18:04
ywilfred wrote:
(-1)^K+1 . (1/2^K). --> The dots mean multiply?

Yes that is correct
Senior Manager
Joined: 01 Sep 2006
Posts: 301
Location: Phoenix, AZ, USA
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

14 Nov 2006, 18:16
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

T1 = (-1)^2*(1/2)^1= 1/2
T2= (-1)^3*(1/2)^2 = -1/4
T3= (-1)^4*(1/2)^3 = + 1/8
.
.
T9= (-1)^10*(1/2)^9= (1/2)^9
t10=(-1)^11*(1/2)^10= - (1/2)^10

ans b/w 1/2 and 1

i think this problem is based on using the knowlege that fractions when multiplied by a fraction the value of product reduces

so 1/2 multiped by 1/2 is less than 1/2
and so on

since 1st term is 1/2 the sume should be greatd than 1/2

if u add rest of the trms the sume will b less than 1/2
ANS B between 1/2 and 1
Manager
Joined: 10 Jul 2006
Posts: 72
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

14 Nov 2006, 18:30
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
Manager
Joined: 12 Jun 2006
Posts: 55
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

15 Nov 2006, 01:48
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?

Thanks
Intern
Joined: 08 Nov 2006
Posts: 35
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

16 Nov 2006, 16:24
1
KUDOS

--------------------------------------------------------------------------------

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

T1 = (-1)^2*(1/2)^1= 1/2
T2= (-1)^3*(1/2)^2 = -1/4
T3= (-1)^4*(1/2)^3 = + 1/8
.
.
T9= (-1)^10*(1/2)^9= (1/2)^9
t10=(-1)^11*(1/2)^10= - (1/2)^10

1/2 - 1/4 = 1/4 + 1/8 = 3/8 - 1/16 = 5/16 + 1/32 = 11 /32 - 1/64 = 21 / 64 + 1/128 = 43 / 128

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.
SVP
Joined: 08 Nov 2006
Posts: 1554
Location: Ann Arbor
Schools: Ross '10
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

16 Nov 2006, 21:43
The series 1/2-1/4+1/8-1/16...is actually a geometric progression with the first term 1/2 and every subsequent term multiplied by -1/2.

a,ar,ar2,.....etc

Sum of 1st n terms of GP = a(1-r^[n+1])/(1-r)

Sum of 10 terms = 1/2(1-(-1/2)^[10+1])/(1-(-1/2) = 0.33

Answer : Between 1/4 and 1/2.

Hope this helps.
Senior Manager
Joined: 29 Jan 2011
Posts: 358
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

24 Jul 2011, 18:39
ncp wrote:
The series 1/2-1/4+1/8-1/16...is actually a geometric progression with the first term 1/2 and every subsequent term multiplied by -1/2.

a,ar,ar2,.....etc

Sum of 1st n terms of GP = a(1-r^[n+1])/(1-r)

Sum of 10 terms = 1/2(1-(-1/2)^[10+1])/(1-(-1/2) = 0.33

Answer : Between 1/4 and 1/2.

Hope this helps.

Isnt the forumula for GP a(1-r^n)/1-r? See youtube video here : http://www.youtube.com/watch?v=OkPI1_BKo9w
Intern
Joined: 19 Jul 2011
Posts: 24
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

25 Jul 2011, 04:30
ncp, what is short way to calculate (1+1/2^11) ? there is gotta be a shortcut..rather than calculating 2^11..
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16470
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

26 Jul 2014, 11:39
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 40281
Re: For every integer k from 1 to 10, inclusive, the kth term of [#permalink]

Show Tags

26 Jul 2014, 11:52
OPEN DISCUSSION OF THIS QUESTION IS HERE: for-every-integer-k-from-1-to-10-inclusive-the-kth-term-of-88874.html
_________________
Re: For every integer k from 1 to 10, inclusive, the kth term of   [#permalink] 26 Jul 2014, 11:52
Similar topics Replies Last post
Similar
Topics:
144 For every integer k from 1 to 10, inclusive, the kth term of a certain 17 17 Jun 2016, 04:50
302 For every integer k from 1 to 10, inclusive, the kth term of 55 25 Jun 2017, 11:06
24 For every integer k from 1 to 10, inclusive the 16 14 Jun 2017, 16:18
for every integer k from 1-10 inclusive, the kth term of a 10 24 Jul 2011, 18:25
1 For every integer k from 1 to 10, inclusive, the kth term of a certain 8 19 Dec 2014, 08:10
Display posts from previous: Sort by

For every integer k from 1 to 10, inclusive, the kth term of

 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®.