Proposition 5

Tag 06C5, permanent. Cite it as [Bourbaki, Tag 06C5].

Algebra, chapter IV, § 4. Formal power series

— In the ring $A[[T]]$ of formal power series in one indeterminate the polynomial $1 - T$ is invertible, and we have $(1 - T)^{-1} = \sum_{n=0}^m T^n$ .

For

(1 - T) \left( \sum_{n=0}^\infty T^n \right) = \sum_{n=0}^\infty T^n - \sum_{n=0}^\infty T^{n+1} = 1.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Proposition 6, § 4
Proposition 1, § 15
§ 1. Definition of Lie algebras

Cites

Nothing.