Section Properties3.
Context {K : AbsRing} {V : NormedModule K}.
exact is_series_scal.
Qed.
exact ex_series_scal.
Qed.
End Properties3.

Lemma is_series_mult (a b : nat -> R) (la lb : R) :
is_series  a la -> is_series  b lb
-> ex_series  (fun n => Rabs (a n)) -> ex_series  (fun n => Rabs (b n))
-> is_series  (fun n => sum_f_R0 (fun k => a k * b (n - k)%nat) n) (la * lb).