Limit of Sequence: Finding the Limit of a Sequence (2)

[izen]

Homework Statement

Find the limit of this sequence

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

Homework Equations

The Attempt at a Solution

The answer is 0 but my answer is 1

thank you

 

[Saitama]

Your first step is wrong.
$$\ln \frac{a}{b}≠\frac{\ln a}{\ln b}$$

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.

 

[izen]

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

Sorry I cannot see how n can factor out from denominator

 

[izen]

like this ??

http://postimage.org/image/7cqb5oowp/ Thanks

 

[izen]

 

[Saitama]

What I actually meant was this:
$$\lim_{n→∞} \frac{1}{n+3} \left( \frac{1}{1+\frac{3}{n}} \right)^n$$

 

[izen]

Thank you