calculate-lim-n-n-ln-n-1-5-n-2-

Question Number 157171 by mathocean1 last updated on 20/Oct/21

c a l c u l a t e \underset{n \to + \infty}{l i m} (\frac{n + l n (n) + 1}{{(5 + \sqrt{n})}^{2}})

Answered by puissant last updated on 20/Oct/21

\lim_{n \to + \infty} (\frac{n + l n (n) + 1}{{(5 + \sqrt{n})}^{2}}) = \lim_{n \to + \infty} (\frac{n (1 + \frac{l n (n)}{n} + \frac{1}{n})}{n {(\frac{5}{\sqrt{n}} + 1)}^{2}})

= \lim_{n \to + \infty} (\frac{1 + \frac{l n (n)}{n} + \frac{1}{n}}{{(\frac{5}{\sqrt{n}} + 1)}^{2}}) = 1 . .

Commented by mathocean1 last updated on 22/Oct/21

t h a n k s l e p u i s s a n t .