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:

Where Kn = * (1/n), and n is represented by a set of [#permalink]

Show Tags

12 May 2008, 11:37

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Where Kn = [-1^(n-1)] * (1/n), and n is represented by a set of integers n = {1, 2, 3, 4, 5 . . . }, what must be true of the sum of the first 20 numbers in Sequence K?

Equal to -1 Equal to 1 Greater than 1 Less than 1 Less than 0

Last edited by jimmyjamesdonkey on 12 May 2008, 13:07, edited 1 time in total.

Where Kn = -1(n-1) (1/n), and n is represented by a set of integers n = {1, 2, 3, 4, 5 . . . }, what must be true of the sum of the first 20 numbers in Sequence K?

Equal to -1 Equal to 1 Greater than 1 Less than 1 Less than 0

Kn = -1(n-1) (1/n) Are we multiplying these two??? b/c if we are its def less than 0 as every number will be negative.

Where Kn = [-1^(n-1)] * (1/n), and n is represented by a set of integers n = {1, 2, 3, 4, 5 . . . }, what must be true of the sum of the first 20 numbers in Sequence K?

Equal to -1 Equal to 1 Greater than 1 Less than 1 Less than 0

If you start to calculate out the sequence, it's something like...

1, -1/2, 1/3, -1/4, etc.

You can group the sequence into groups of 2. The sum of each group is positive, but smaller than half of the previous group sum (with the first sum group = 1/2). Therefore, the total sum will be positive, but less than 1.

Where Kn = [-1^(n-1)] * (1/n), and n is represented by a set of integers n = {1, 2, 3, 4, 5 . . . }, what must be true of the sum of the first 20 numbers in Sequence K?

Equal to -1 Equal to 1 Greater than 1 Less than 1 Less than 0

-1^(n-1)*1/n Lets start off w/ the first number 1.

-1^(0)*1 --> 1

Next is -1/2 After that its 1/3 After that its -1/4

I would stop here, b/c going to 20 is obviously too time consuming. We can gather something here though 1-1/2+1/3-1/4=.58333

Here we can realize the numbers are going to get small and smaller. To the point where its almost insignificant. Id say D at this point.

I'm not sure. I just did it for this particular problem, because it helped me simplify and structure the problem.

Other cases I would group numbers would be adding up a series, let's say, and by pairing up numbers, you could find a pattern. An example would be adding up 1 thru 100. You can pair it up into 50 pairs of sum 101: (1+100), (2+99), (3+98), etc.