# Proof Without Words: Geometric Series Formula

by James Tanton

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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