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I have a series like this:

$$1 + \frac 1 {x^2} + \frac 1 {x^4} + \frac 1 {x^6} ....$$

Is this a known series? Can I simplify this to something?

Thanks.

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    It is a geometric series.2011-10-10
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    Your series is just a geometric series, $\sum_{n = 0}^{\infty} x^{-2n} = \sum_{n = 0}^{\infty} (x^{-2})^n$.2011-10-10

1 Answers 1

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If $|x|\gt 1$ your series will converge. You can put $y=x^2$ and it is a standard geometric series

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    You mean $|x| > 1$.2011-10-10
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    @RobertIsrael: Right. In the denominator2011-10-10