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]
11 Aug 2007, 12:14

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

53% (03:05) correct
47% (01:46) wrong based on 56 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

Re: For every integer k from 1 to 10, inclusive, the kth term of a certain [#permalink]
11 Aug 2007, 12:22

zakk wrote:

1) 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 of the sequence, then T is:

a) greater than 2 b) between 1 and 2 c) between ½ and 1 d) between ¼ and ½ e) less than ¼

I guess right, but have no idea on the concept behind this.

Can you clarify (-1)^k+1 (1/2^k)?
Is it ((-1)^(k+1)) * (1/(2^K))?

Re: For every integer k from 1 to 10, inclusive, the kth term of a certain [#permalink]
11 Aug 2007, 13:56

assuming its the later case -1^(K+1)

then its basically saying that for every odd K, the term would be positive and even term would be negative, however net result would they still cancel out...in that case the sum would be 1/2+1/4+1/8...i.e C

bkk145 wrote:

zakk wrote:

1) 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 of the sequence, then T is:

a) greater than 2 b) between 1 and 2 c) between ½ and 1 d) between ¼ and ½ e) less than ¼

I guess right, but have no idea on the concept behind this.

Can you clarify (-1)^k+1 (1/2^k)? Is it ((-1)^(k+1)) * (1/(2^K))?

Re: For every integer k from 1 to 10, inclusive, the kth term of a certain [#permalink]
11 Aug 2007, 14:16

I agree with emarinich - and that's a great explanation, btw!

The first nmber in the sequence is 1/2, then -1/4, 1/8, etc. It increases or decreases by an exponentially smaller number each time, so matter how far you carry it, the sum will never equal a number greater than the first number, so must be between 1/4 and 1/2. Actually this same problem was posted a week or so ago - challenging and fascinating!

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

A site for the partners of MBA candidates : A website we are creating for the better halves of the MBA candidates and the candidates themselves to know “the...

A week ago we were informed of our pre program preparation for Entrepreneurship and Finance… 2.5 months to go and we are already busy with our studies… Where...