Simplifying a series

Question

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.

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

Ross Millikan · Accepted Answer · 2011-10-10T22:49:15.783

9

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

edited Oct 10 '11 at 22:49

answered Oct 10 '11 at 22:26

Ross Millikan

1 Answers1