(** * Convergence theorems *)

(* Specifications: *)
Lemma Cauchy_series_Reals (a : nat -> R) :
Cauchy_series a <-> Cauchy_crit_series a.
Lemma ex_series_lim_0 (a : nat -> R) :
ex_series a -> is_lim_seq a 0.
Lemma ex_series_Rabs (a : nat -> R) :
ex_series (fun n => Rabs (a n)) -> ex_series a.
Lemma Series_Rabs (a : nat -> R) :
ex_series (fun n => Rabs (a n)) ->
Rabs (Series a) <= Series (fun n => Rabs (a n)).