We have calculated static and dynamic longitudinal polarizabilities, alpha(zz)(-omega;omega), for the polyyne series, C2nH2, using both the uncorrelated random phase approximation and the correlated second-order polarization propagator approximation. The calculated polarizabilities are extrapolated to the value for the infinitely long chain using seven different extrapolation techniques. We employ both conventional schemes, such as the fitting of simple polynomials, as well as new schemes, such as the fitting of a Pade approximant, or purely mathematically motivated nonlinear sequence transformations which have not previously been used in connection with this property. For the direct fits, where the number of parameters is the same as the number of points, we find that the most stable and reliable extrapolation schemes are to be found among the latter.