The formal series has inverse element iff .
If is the inverse of the formal series then, the equality will provide:
So, you can determine .
the problem is to calculate inverse element (reciprocal) of in ring .
I skimmed some Wikipedia and found following formula:
But I don't know to use it. Also the following model answer didn't help me either:
"Task is to calculate inverse element (reciprocal) of in the ring .
So, we have to calculate that
When the is solved, and then ..., we see that inverse element is "
I don't understand how those etc. are solved. Only thing, that is clear to me is, that is generated by , which equals .
So, any help is appreciated. Thanks very much!