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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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Local Open Scope R_scope.
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(* Various versions of the criterion of D'Alembert *)
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(** A useful criterion of convergence for power series *)
Theorem Alembert_C3 :
forall (An:nat -> R) (x:R),
(forall n:nat, An n <> 0) ->
Un_cv (fun n:nat => Rabs (An (S n) / An n)) 0 ->
{ l:R | Pser An x l }.