Definition series_cv_abs {R : ConstructiveReals} (u : nat -> CRcarrier R)
  : CR_cauchy R (CRsum (fun n => CRabs R (u n)))
    -> { l : CRcarrier R & series_cv u l }.

Lemma series_cv_remainder_maj : forall {R : ConstructiveReals} (u : nat -> CRcarrier R) (s eps : CRcarrier R) (N : nat), series_cv u s -> 0 < eps -> (forall n:nat, 0 <= u n) -> CRabs R (CRsum u N - s) <= eps -> forall n:nat, CRsum (fun k=> u (N + S k)%nat) n <= eps.