General proof of a limit related to AR(k) model of Statistics

Computing moments of various parameter estimators related to an autoregressive model of Statistics, one needs to evaluate several non-trivial limits. This was done by arXiv:1506.03131 for the case of two, three and four dimensions; in this article, we present a proof of a fully general formula, based on an ingenious solution of https://mathoverflow.net/users/4312/fedor-petrov.