Question

Please help me ... limit to infinity of ln (n+1) / ln n

Answer 1

use l'hopital's rule here ^_^:

\[\lim_{x \rightarrow \infty} {\frac{1}{n+1}}(n) = \lim_{x \rightarrow \infty} \frac{n}{n} = 1\]

^_^

Answer 2

did you understand it? :)

Answer 3

so, Ln (n + 1) / Ln n = Ln [(n+1) / n] , right or wrong? I don't have any clue.

Answer 4

Since you have something in the form of \(\infty/\infty\) you need to use l'Hopital's rule. Which is that the limit of the original ratio is the limit of the ratio of the derivatives.
if \((\lim_{n \rightarrow \infty} f(n)= \lim_{n \rightarrow \infty} g(n)) \in \{\infty,0\} \)
\[\lim_{n \rightarrow \infty}\frac{f(n)}{g(n)} = \lim_{n \rightarrow \infty} \frac{f'(n)}{g'(n)}\]

The derivative of ln(n) = \(\frac{1}{n}\)
The derivative of ln(n+1) = \(\frac{1}{n}\)
So the ratio of the derivatives will be
\[\frac{\frac{1}{n}}{\frac{1}{n}} = \frac{n}{n} = 1\]
And the \(\lim_{n \rightarrow \infty} 1 = 1\)

Answer 5

Thanks for your help :)