For-k-lt-N-fixed-and-gt-0-then-lim-n-1-n-i-1-k-n-k-i-i-1-k-n-i-n-

Question Number 150548 by mathdanisur last updated on 13/Aug/21

For k < N fixed and α > 0 then :

\lim_{n \to \infty} \frac{1}{\sqrt{n^{α}}} \cdot {(\frac{\underset{i = 1}{\prod^{k}} (n + k + i)}{\underset{i = 1}{\prod^{k}} (n + i)})}^{n^{α}}