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What is this series?

Eliot Rosewater · 2011-01-26 15:55:34

Hi! Just a quick question. I'm working though a Number Theory book I bought, and the authors make use of the following series: [LATEX]\displaystyle \frac{a^{kl}+1}{a^{l}+1}=a^{(k-1)l}-a^{(k-2)l}+ . . . + 1[/LATEX] where k is odd and l is a power of 2. Does anyone know what kind of series expansion this is? Google won't…

26-01-2011 3:55pm

#1

Eliot Rosewater

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Hi! Just a quick question. I'm working though a Number Theory book I bought, and the authors make use of the following series:

[LATEX]\displaystyle \frac{a^{kl}+1}{a^{l}+1}=a^{(k-1)l}-a^{(k-2)l}+ . . . + 1[/LATEX]

where k is odd and l is a power of 2.

Does anyone know what kind of series expansion this is? Google won't accept Latex searches.

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Comments

#2 26-01-2011 4:12pm

Fremen

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It's a geometric series with common ratio -a^L, or the difference of two geometric series with common ratio a^{2L}.

I have a feeling you're going to kick yourself when you read this

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#3 26-01-2011 11:11pm

Eliot Rosewater

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Yup - silly silly me! Cheers Fremen!

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