Pages of circles On page 1 of a book, there is one circle

Chapter 1, Problem 55RE

(choose chapter or problem)

Pages of circles On page 1 of a book, there is one circle of radius 1. On page 2, there are two circles of radius \(\frac{1}{2}\). On page n there are \(2^{n-1}\) circles of radius \(2^{-n+1}\).

a. What is the sum of the areas of the circles on page n of the book?

b. Assuming the book continues indefinitely \((n \rightarrow \infty)\), what is the sum of the areas of all the circles in the book?

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back