evaluate-the-following-limit-if-it-exists-lim-n-ln-2-n-1-n-1-2-

Question Number 169514 by Giantyusuf last updated on 01/May/22

e v a l u a t e t h e f o l l o w i n g l i m i t

(i f i t e x i s t s)

{l i m}_{n \to \infty} \frac{{l n}^{2} (n + 1)}{{(n - 1)}^{2}}

Commented by Giantyusuf last updated on 01/May/22

y o u r s o l u t i o n ?

Commented by greougoury555 last updated on 02/May/22

\lim_{n \to \infty} \frac{\ln^{2} (n + 1)}{{(n - 1)}^{2}} = {(\lim_{n \to \infty} \frac{\ln (n + 1)}{n - 1})}^{2}

l e t \ln (n + 1) = u \Rightarrow n = e^{u} - 1

{(\lim_{u \to \infty} \frac{u}{e^{u} - 2})}^{2} = {(\lim_{u \to \infty} \frac{1}{e^{u}})}^{2} = 0

Answered by Mathspace last updated on 01/May/22

= {l i m}_{n \to + \infty} {(\frac{l n (n)}{n})}^{2} = 0