Convergent Series of Rectangles to Fill a Unit Square

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows graphically how the sum of a certain infinite series converges to 1. Blue rectangles are successively added inside a square of area 1. Each iteration shades a fraction (numerator , denominator ) of the unshaded region of the square. The shaded rectangle has area given recursively by with , so that . The area after rectangles have been shaded is given recursively by with . Thus , which tends to 1 as .

Contributed by: Jeremy Kogan (March 2017)
Inspired by: Jonathan Kogan
Open content licensed under CC BY-NC-SA




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.