# Convergent Series of Rectangles to Fill a Unit Square

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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

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detailSectionParagraph## Permanent Citation

"Convergent Series of Rectangles to Fill a Unit Square"

http://demonstrations.wolfram.com/ConvergentSeriesOfRectanglesToFillAUnitSquare/

Wolfram Demonstrations Project

Published: March 7 2017