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

(* 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.