I've encountered this limit on a book without solution and after two days of thinking still I am not able to come up with an answer.
$\lim_{n\to+\infty}\left(\alpha k^{\frac 1n}-1\right)^n,\: k\in\mathbb R_{>0},\: \alpha\in\mathbb N_{>0}.$
A full complete and detailed soultion is welcomed. Also hints of course are accepted.
I've tried binomial Formula and to simplify the expression but all has been in vain.