1 Attachment(s)

Series expansion question.

The first part i had no trouble with.

Its just the explanation for part 2 for why it is not possible to express $\displaystyle g(x)$ as a series of non-negative powers of x. I was thinking it could be related to $\displaystyle g(x)$ being undefined at $\displaystyle x=0 $ but then it can still be expressed as a series of non-negative power of (x-a) though, and why does it work for $\displaystyle xg(x)$? i am struggling to give a decent explanation for this part

Thanks

Bobak