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_n_ext :
forall (a b : nat -> G) N,
(forall n, a n = b n) ->
sum_n a N = sum_n b N.