induction n2; intuition; unfold sumList; simpl in *.
intuition.
rewrite fold_add_body_eq.
2:{
eapply ratAdd_comm.
}
rewrite fold_add_init.
unfold sumList in *.
rewrite IHn2; eauto.
eapply eqRat_trans.
2:{
symmetry.
eapply eqRat_trans.
eapply fold_add_body_eq.
eapply ratAdd_comm.
intuition.
eapply eqRat_refl.
eapply fold_add_init.
}
eapply ratAdd_eqRat_compat.
eauto.
intuition.
intuition.
Qed.

Lemma sumList_series_split_first : forall n f,
sumList (n :: getNats O n) f == f O + (sumList (getNats 1 n) f).