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.


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Sums of Geometric Series - Proofs Without Words


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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


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