Analytical continuation of Taylor series

Let us expand $\sqrt{1-x^2}$ in Taylor series...



I get an error when evaluating this code, saying that ** should be used for exponentiation instead of ^.  If I change the carets on lines 7 and 29 to double stars, then the errors go away, even though I can see several other uses of the caret in the code . . . strange.

Youp  - and I think this error was absent at the time I posted this interact.
Anyways - I have changed all ^ to ** and it it fine ;-)