- #1

- 176

- 0

I was workin on a problem and during my proof I came to this problem does anybody know what happens with this limit

[tex]\lim_{n\rightarrow\infty} \frac{\log {(n+1)}}{\log {n}}[/tex]

thanxs

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter steven187
- Start date

- #1

- 176

- 0

I was workin on a problem and during my proof I came to this problem does anybody know what happens with this limit

[tex]\lim_{n\rightarrow\infty} \frac{\log {(n+1)}}{\log {n}}[/tex]

thanxs

- #2

matt grime

Science Advisor

Homework Helper

- 9,395

- 4

HINT: n+1 = n(1+1/n)

- #3

- 176

- 0

would this be correct?

[tex]\lim_{n\rightarrow\infty} \frac{\log {(n+1)}}{\log {n}}[/tex]

[tex]=\lim_{n\rightarrow\infty} \frac{\log {n(1+\frac{1}{n})}}{\log {n}}[/tex]

[tex]=\lim_{n\rightarrow\infty} \frac{\log{n}+\log {n(1+\frac{1}{n})}}{\log {n}}[/tex]

[tex]=1+\lim_{n\rightarrow\infty} \frac{\log {(1+\frac{1}{n})}}{\log {n}}=1[/tex]

- #4

- 537

- 1

yes that looks right except that you have a typo in the 3rd equation.

Share:

- Replies
- 2

- Views
- 1K