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(**  *       Definition of Power Series and properties           *)
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Section Isequence.
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Variable An : nat -> R.
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Definition Pser (x l:R) : Prop := infinite_sum (fun n:nat => An n * x ^ n) l.
End Isequence.

(* Specifications: *)
Lemma GP_infinite :
forall x:R, Rabs x < 1 -> Pser (fun n:nat => 1) x (/ (1 - x)).
(* Convergence is preserved after shifting the indices. *)
Lemma CV_shift :
forall f k l, Un_cv (fun n => f (n + k)%nat) l -> Un_cv f l.