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.

Lemma PSeries_scal (c : R) (a : nat -> R) (x : R) :
PSeries (PS_scal c a) x = c * PSeries a x.