Show that (1+x)^-1=1+x+x^2+...in the series ring R[[x]]?
- Anonymous1 decade agoFavorite Answer
That should be, (1-x)^-1 = 1 + x + x^2 + ...
Or, (1+x)^-1 = 1 - x + x^2 - x^3 + ...
Both are true, but the original is not.
And either can be proven, first by showing that inverses in rings, whenever they exist, are unique, and then that the product of any element of a ring, and its inverse, equals the identity, 1.