We report on the systematic study of infrared/terahertz spectra of photocurrents in (Bi, Sb) Te based three-dimensional topological insulators. We demonstrate that in a wide range of frequencies, ranging from fractions up to tens of terahertz, the photocurrent is caused by the linear photogalvanic effect (LPGE) excited in the surface states. The photocurrent spectra reveal that at low frequencies the LPGE emerges due to free carrier Drude-like absorption. The spectra allow us to determine the room temperature carrier mobilities in the surface states despite the presence of thermally activated residual impurities in the material bulk. In a number of samples we observed an enhancement of the linear photogalvanic effect at frequencies between 30 and 60 THz, which is attributed to the excitation of electrons from helical surface to bulk conduction band states. Under this condition and applying oblique incidence we also observed the circular photogalvanic effect driven by the radiation helicity.