| 1. | Archimedes succeeded in summing what is now called a geometric series.
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| 2. | The Neumann series, which is analogous to the geometric series
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| 3. | It's how you simplify the geometric series, for instance.
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| 4. | The same strategy works for any finite geometric series.
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| 5. | Applying the formula for geometric series, we get
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| 6. | This is a geometric series with common ratio 1 / ( 1 + I ).
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| 7. | Then we reduce it to some form of geometric series and find the Laurent series.
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| 8. | In that example we used the geometric series
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| 9. | The geometric series model fits observed species abundances in highly uneven communities with low diversity.
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| 10. | However, by summing a geometric series this expression can be expressed in the closed-form:
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