Sums of Geometric Series - Proofs Without Words

The applet below illustrates three identities - sums of geometric series - with factors 1/2, 1/3, and 1/4, namely,

2^-1 + 2^-2 + 2^-3 + 2^-4 + ... = 1,
3^-1 + 3^-2 + 3^-3 + 3^-4 + ... = 1/2,
4^-1 + 4^-2 + 4^-3 + 4^-4 + ... = 1/3.

---

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

---

Credits: The proofs for factors 1/2 (Warren Page) and 1/4 (Sunday A. Ajose) have been published previously; both have been included into R. B. Nelsen's Proofs Without Words.

Reference

1. R. B. Nelsen, Proofs Without Words, MAA, 1993

Proofs Without Words

• Proofs Without Words
• Sums of Geometric Series - Proofs Without Words
• Sine of the Sum Formula
• Parallelogram Law: A PWW
• Parallelogram Law
• Ceva's Theorem: Proof Without Words
• Viviani's Theorem
• A Property of Rhombi
• Triangular Numbers in a Square
• PWW: How Geometry Helps Algebra

|Activities| |Contact| |Front page| |Contents| |Algebra| |Store|

Copyright © 1996-2012 Alexander Bogomolny