Show that for large n this estimate of rho is equal to the

Question

Theil and Nagar have suggested that in small samples instead of estimating ρ as (1 - d/2), it be estimated as

ρˆ =((1 - d/2) + k²/n²)/1-n²/k²

where n = total number of observations, d = Durbin-Watson d, and k = number of coef?cients (including the intercept) to be estimated.

Show that for large n, this estimate of ρ is equal to the one obtained by the simpler formula (1 - d/2).