Section Properties3.
Context {K : AbsRing} {V : NormedModule K}.
exact is_series_scal.
Qed.
exact ex_series_scal.
Qed.
End Properties3.
(** * D'Alembert criterion *)

Lemma ex_series_DAlembert (a : nat -> R) (k : R) :
k < 1 -> (forall n, a n <> 0)
-> is_lim_seq (fun n => Rabs (a (S n) / a n)) k
-> ex_series  (fun n => Rabs (a n)).