Originally Posted by

**iva** I hope this is the right forum for this, it is a differential equations I'm doing, with series now which I'm reviewing before getting into the calculus of it.

I have to find the radius and interval of convergence for this series, and i'm using a ratio test but I can't get past a certain point. my original equation is:

$\displaystyle \sum_{n=1}^{\infty} \frac {(-1)^{n-1} x^{2n-1}} {(2n-1)!} $

I then applied the ratio test (i.e. n+1 series on top and original series on the bottom) and get this far:

$\displaystyle \lim_{n}^{\infty} \frac{-x}{2n} = \frac{-x}{2}\lim_{n}^{\infty} \frac{1}{n} $

Seeing as its the harmonic series whose sum is infinity i am baffled at how to simplify this so i can continue with my equation to get my radius and interval of conversion.

Any advice really appreciated

Thank you