(** Definition of ps_atan's derivative *)

Definition Datan_seq := fun (x : R) (n : nat) => x ^ (2*n).

Lemma Datan_sum_eq :forall x n, sum_f_R0 (tg_alt (Datan_seq x)) n = (1 - (- x ^ 2) ^ S n)/(1 + x ^ 2).