Definition PS_derive_n (n : nat) (a : nat -> R) :=
  (fun k => (INR (fact (k + n)%nat) / INR (fact k)) * a (k + n)%nat).

Lemma ex_derive_n_PSeries (n : nat) (a : nat -> R) (x : R) : Rbar_lt (Finite (Rabs x)) (CV_radius a) -> ex_derive_n (PSeries a) n x.