• Support PF! Buy your school textbooks, materials and every day products Here!

Limit of sequence (2)

  • Thread starter izen
  • Start date
  • #1
51
0

Homework Statement



Find the limit of this sequence

An =[itex] \frac{n^{n}}{(n+3)^{n+1}}[/itex]

Homework Equations




The Attempt at a Solution



infinite_limit.jpg


The answer is 0 but my answer is 1

thank you
 

Answers and Replies

  • #2
3,812
92
Your first step is wrong.
[tex]\ln \frac{a}{b}≠\frac{\ln a}{\ln b}[/tex]

The correct property is:
[tex]\ln \frac{a}{b}= ln a-\ln b[/tex]

Anyways, instead of taking log on both the sides, you can factor out n from denominator.
 
  • #3
51
0
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
 
  • #4
51
0
like this ??

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


Thanks
 
Last edited by a moderator:
  • #5
51
0
limit_2.jpg
 
  • #6
3,812
92
What I actually meant was this:
[tex]\lim_{n→∞} \frac{1}{n+3} \left( \frac{1}{1+\frac{3}{n}} \right)^n[/tex]
 
  • #7
51
0
Thank you
 

Related Threads for: Limit of sequence (2)

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
951
Replies
4
Views
2K
  • Last Post
Replies
9
Views
5K
Replies
3
Views
609
  • Last Post
Replies
6
Views
9K
  • Last Post
Replies
6
Views
4K
  • Last Post
Replies
6
Views
7K
Top