reserve a,b,c,d for positive Real,
  m,u,w,x,y,z for Real,
  n,k for Nat,
  s,s1 for Real_Sequence;

theorem
  (for n holds s.n=1/((n+1)^2)) implies (Partial_Sums s).n<2
proof
  assume for n holds s.n=1/((n+1)^2);
  then
A1: (Partial_Sums s).n<=2-1/(n+1) by Th48;
  -(1/(n+1))+2<0+2 by XREAL_1:8;
  hence thesis by A1,XXREAL_0:2;
end;
