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

Lemma Derive_n_PSeries (n : nat) (a : nat -> R) (x : R) :
Rbar_lt (Finite (Rabs x)) (CV_radius a)
-> Derive_n (PSeries a) n x = PSeries (PS_derive_n n a) x.