FREE Trial

There is one circle of radius 1. There are two circles of radius 1/2. There are 2

Question:

There is one circle of radius 1. There are two circles of radius 1/2. There are 2n - 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→∞), what is the sum of the areas of all the circles in the book?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Answer rating: 85% (7 reviews)

a The area of a circle of radius r is r For ...View the full answer


answer-question
Answered By
tutor-profile-image
Nazrin Ziad
I am a post graduate in Zoology with specialization in Entomology.I also have a Bachelor degree in Education.I posess more than 10 years of teaching as well as tutoring experience.I have done a project on histopathological analysis on alcohol treated liver of Albino Mice. I can deal with every field under Biology from basic to advanced level.I can also guide you for your project works related to biological subjects other than tutoring.You can also seek my help for cracking competitive exams with biology as one of the subjects.
3.30+ 2+ Reviews 10+ Question Solved
Related Book For  answer-question
Calculus Early Transcendentals

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

See More Books
Question Posted:
See More Questions

Related Video

The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.

Students also viewed these Mathematics questions

Emotional Intelligence For Stress Free Leadership Turn Emotional Pain Into Performance Gain With The Tenor Method 1st Edition - ISBN: B088T2KJ3D - Free Book