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

Lemma PI_ineq : forall N : nat,
sum_f_R0 (tg_alt PI_tg) (S (2 * N)) <= PI/4 <= sum_f_R0 (tg_alt PI_tg) (2 * N).