Section PS_scal.
Context {K : AbsRing} {V : NormedModule K}.
Definition PS_scal (c : K) (a : nat -> V) (n : nat) : V := scal c (a n).
End PS_scal.
Definition PS_scal_r (c : R) (a : nat -> R) (n : nat) : R :=
a n * c.

Lemma PSeries_scal_r (c : R) (a : nat -> R) (x : R) :
PSeries (PS_scal_r c a) x = PSeries a x * c.