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

Lemma ex_pseries_plus (a b : nat -> V) (x : K) :
ex_pseries a x -> ex_pseries b x
-> ex_pseries (PS_plus a b) x.