sum(1/(n^4+n^2+n),n=1..infinity);

  -infinity

                         /   -----                               \
                         |    \                2                 |
        signum(-1 + 1/31 |     )      (4 _alpha  + 13 - 6 _alpha)|)
                         |    /                                  |
                         |   -----                               |
                         \_alpha = %1                            /

         + gamma + 1/31

        /   -----                                               \
        |    \                2                                 |
        |     )      (4 _alpha  + 13 - 6 _alpha) Psi(1 - _alpha)|
        |    /                                                  |
        |   -----                                               |
        \_alpha = %1                                            /

                 3
  %1 := RootOf(_Z  + _Z + 1)

evalf(%);

                Float(undefined) + Float(undefined) I

evalf(subsop(1=0,%%));

                         0.3966190358 + 0. I

evalf(Sum(1/(n^4+n^2+n),n=1..infinity));

                             0.3966190358

Alec