# Limit of sequence (2)

1. Feb 8, 2013

### izen

1. The problem statement, all variables and given/known data

Find the limit of this sequence

An =$\frac{n^{n}}{(n+3)^{n+1}}$

2. Relevant equations

3. The attempt at a solution

thank you

2. Feb 8, 2013

### Saitama

$$\ln \frac{a}{b}≠\frac{\ln a}{\ln b}$$

The correct property is:
$$\ln \frac{a}{b}= ln a-\ln b$$

Anyways, instead of taking log on both the sides, you can factor out n from denominator.

3. Feb 8, 2013

### izen

Sorry I cannot see how n can factor out from denominator

4. Feb 8, 2013

### izen

like this ??

http://postimage.org/image/7cqb5oowp/ [Broken]

Thanks

Last edited by a moderator: May 6, 2017
5. Feb 8, 2013

6. Feb 9, 2013

### Saitama

$$\lim_{n→∞} \frac{1}{n+3} \left( \frac{1}{1+\frac{3}{n}} \right)^n$$