reserve n,m,k for Nat;
reserve a,p,r for Real;
reserve s,s1,s2,s3 for Real_Sequence;

theorem Th21:
  s is summable iff for r st 0<r ex n st for m st n<=m holds |.
  Partial_Sums(s).m - Partial_Sums(s).n.|<r
by SEQ_4:41;
