I need to find out if the Alternating Series is convergent or divergent by the Alternating Series Test.

One condition is to check if the limit is zero.

I have problems finding the limit, since I have a term (2k-1)! in the denominator and I do not know how to handle this...

How can I write the fraction, so that things cancel out?

For the following example I was able to write one term:

Can someone please let me know how to do this with

Thanks!