reserve a,b,c for set;
reserve r for Real,
  X for set,
  n for Element of NAT;

theorem Th23:
  Sum (((1/2) GeoSeq)^\(n+1)) = (1/2)|^n
proof
  set r = 1/2;
  thus Sum (((1/2) GeoSeq)^\(n+1)) = (r|^(n+1)) / (1-r) by Th22
    .= (1/2)|^n*r/r by NEWTON:6
    .= r|^n;
end;
