Section ConvergenceCircle.
Context {K : AbsRing} {V : NormedModule K}.
End ConvergenceCircle.
(** Convergence disk *)
Definition CV_disk (a : nat -> R) (r : R) :=
ex_series (fun n => Rabs (a n * r^n)).
Definition CV_radius (a : nat -> R) : Rbar :=
Lub_Rbar (CV_disk a).

Lemma CV_radius_bounded (a : nat -> R) :
is_lub_Rbar (fun r => exists M, forall n, Rabs (a n * r ^ n) <= M) (CV_radius a).