(** * Power series *)
Definition PS_Int (a : nat -> R) (n : nat) : R :=
match n with
| O => 0
| S n => a n / INR (S n)
end.

Lemma RInt_PSeries (a : nat -> R) (x : R) :
Rbar_lt (Rabs x) (CV_radius a)
-> RInt (PSeries a) 0 x = PSeries (PS_Int a) x.