Section Sums.
Context {G : AbelianGroup}.
Definition sum_n_m (a : nat -> G) n m :=
iter_nat plus zero a n m.
Definition sum_n (a : nat -> G) n :=
sum_n_m a O n.

Lemma sum_Sn (a : nat -> G) (n : nat) :
sum_n a (S n) = plus (sum_n a n) (a (S n)).