restart; interface(version);
  Digits:=14;
  Classic Worksheet Interface, Maple 12.02, Windows, Dec 10 2008 Build ID 377066

                             Digits := 14

  Psi(1/8): 
  %=convert(%, Sum); # compare the FunctionAdvisor as well ...
  evalf(%);
 
                      infinity
                       -----   /        _k2              \
                        \      |    (-1)    Zeta(_k2 + 2)|
           Psi(1/8) =    )     |1/8 ---------------------|
                        /      |             _k2         |
                       -----   \            8            /
                      _k2 = 0


                 -8.3884926632959 = 0.18872300160568


Or some more examples:

  c:=0;
  [seq(1/n + c, n=1..19)];
  map(Psi, %);
  map( 't -> t=convert(t, Sum, only=Psi, dummy=k)', %);
  evalf[2*Digits](%);
  map(fnormal, %);
  map(is, %);

       [true, true, true, true, false, true, false, false, false, false,
        false, false, false, false, false, false, false, false, false]


That's not only false for rationals (try c = 1/exp(1)).