(** Sums on even and odd *)

Lemma PSeries_odd_even (a : nat -> R) (x : R) :
ex_pseries (fun n => a (2*n)%nat) (x^2) -> ex_pseries (fun n => a (2*n+1)%nat) (x^2)
-> PSeries a x = PSeries (fun n => a (2*n)%nat) (x^2) + x * PSeries (fun n => a (2*n+1)%nat) (x^2).