Work Done Inserting Dielectric with Battery Disconnected

Initial energy $$U_i = \frac{Q^2}{2C_0}$$, final energy $$U_f = \frac{Q^2}{2KC_0}$$,
Work done by capacitor: $$W = U_i - U_f = \frac{Q^2}{2C_0}\left(1 - \frac{1}{K}\right)$$
Charge $$Q$$ constant (battery disconnected). $$C_0$$: initial capacitance.