(** Definition of ps_atan's derivative *)
Definition Datan_seq := fun (x : R) (n : nat) => x ^ (2*n).

Lemma Ratan_is_ps_atan : forall eps, eps > 0 ->
exists N, forall n, (n >= N)%nat -> forall x, -1 < x -> x < 1 ->
Rabs (sum_f_R0 (tg_alt (Ratan_seq x)) n - ps_atan x) < eps.