Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
2  
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
add comment

1 Answer

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

share|improve this answer
2  
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
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.