Section Isequence.
(*********)
Variable An : nat -> R.
(*********)
Definition Pser (x l:R) : Prop := infinite_sum (fun n:nat => An n * x ^ n) l.
End Isequence.

Lemma GP_infinite :
forall x:R, Rabs x < 1 -> Pser (fun n:nat => 1) x (/ (1 - x)).