induction ls; intuition.
unfold sumList.
simpl.
econstructor.
intuition.
unfold sumList in *. simpl in *.
econstructor.
eapply IHls.
eapply eqRat_refl.
rewrite fold_add_body_eq.
2:{
eapply ratAdd_comm.
}
rewrite fold_add_init.
eapply eqRat_refl.
intuition.
Qed.

Lemma sumList_series_incr : forall n2 n1 (f f' : nat -> Rat),
(forall n, (f n) == (f' (S n))) ->
sumList (getNats n1 n2) f == sumList (getNats (S n1) n2) f'.