I've come across a snag in a proof, and I've become a little exasperated by the following limit:
\displaystyle \lim_{p\to\infty} \biggl(\frac{{| d |}^{np+p-1} |x|^{p-1}}{(p-1)!} \{(|x| + |\alpha_1|) \ldots (|x| + |\alpha_n|) \}^p\biggr)
I've tried the squeeze rule, but an upper bound...