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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?


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It is a geometric series. – Phira Oct 10 '11 at 22:25
Your series is just a geometric series, $\sum_{n = 0}^{\infty} x^{-2n} = \sum_{n = 0}^{\infty} (x^{-2})^n$. – Adrián Barquero Oct 10 '11 at 22:27
up vote 9 down vote accepted

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 $|x| > 1$. – Robert Israel Oct 10 '11 at 22:29
@RobertIsrael: Right. In the denominator – Ross Millikan Oct 10 '11 at 22:49

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