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Proof Without Words: Geometric Series Formula

by James Tanton

This article originally appeared in:
College Mathematics Journal
March, 2008

Subject classification(s): Calculus | Single Variable Calculus | Series
Applicable Course(s): 3.2 Mainstream Calculus II | 3.5 Non-mainstream Calc II

The result is illustrated for ratio 1/9, via an approach that is readily generalized.  In particular, the result \( \frac{1}{n} + \frac{1}{n^2}  + \frac{1}{n^3} + \cdots = \frac{1}{n-1} \) is illustrated for \( n = 9 \), and the remark is made that a similar construction shows the result for any integer \(n \), \(n \geq 2 \).

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Capsule Course Topic(s):
Sequences and Series | Special Series: Geometric Series
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