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.