Section PS_plus.
Context {K : AbsRing} {V : NormedModule K}.
Definition PS_plus (a b : nat -> V) (n : nat) : V := plus (a n)  (b n).
End PS_plus.

Lemma PSeries_plus (a b : nat -> R) (x : R) :
ex_pseries a x -> ex_pseries b x
-> PSeries (PS_plus a b) x = PSeries a x + PSeries b x.