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 350,000 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 [#permalink]
03 Jun 2007, 02:27

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

58% (02:41) correct
42% (01:38) wrong based on 87 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

suppose
S=1+1/2+1/4+1/8............................ this is an infinite GP and here
s comes to be S=2(which is max).
Now we are given
S=1/2-1/4+1/8-1/16+...........
here solving for first two terms we get 1/4 i.e .25 means our answer should be greater than .25 as all other terms gives positive in pair of two.
Now the max. value of this expansion will be 1 when all the terms are positive and upto infinite but in this every alternate term is negative thus reducing the sum of expansion to half of 1 that is 1/2(.5) which can be the max. value.
Thus value lies b/w .25 and .50.

suppose S=1+1/2+1/4+1/8............................ this is an infinite GP and here s comes to be S=2(which is max). Now we are given S=1/2-1/4+1/8-1/16+........... here solving for first two terms we get 1/4 i.e .25 means our answer should be greater than .25 as all other terms gives positive in pair of two. Now the max. value of this expansion will be 1 when all the terms are positive and upto infinite but in this every alternate term is negative thus reducing the sum of expansion to half of 1 that is 1/2(.5) which can be the max. value. Thus value lies b/w .25 and .50.

D should be the answer.

Good explanation. Answer is correct. But please remember it is not "infnite G.P." Up to 10 terms only.

For every integer k from 1 to 10, inclusive, the kth term... [#permalink]
04 Aug 2013, 11:05

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

Last edited by Zarrolou on 04 Aug 2013, 11:07, edited 1 time in total.

Re: For every integer k from 1 to 10, inclusive, the kth term... [#permalink]
04 Aug 2013, 11:24

Expert's post

njkhokh 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

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

From the given sum, T \(= \frac{1}{2}-\frac{1}{2^2}.......-\frac{1}{2^{10}}\)

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...