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

Ratio Test

  • Thread starter jeffreylze
  • Start date
  • #1
44
0

Homework Statement


http://img132.imageshack.us/img132/6663/captureqqi.jpg [Broken]

Homework Equations





The Attempt at a Solution



I came up with this answer and i dont know how to continue:

(1+1/n)^n

I understand I have to put in limit n -> infinty. But can i put the limit inside the bracket? So i will get an answer of 1 ?

So ultimately, the ratio test is inconclusive?
 
Last edited by a moderator:

Answers and Replies

  • #2
dx
Homework Helper
Gold Member
2,011
18
(1 + (1/n))n → e (≈ 2.718) as n → ∞.
 
  • #3
44
0
How did you get that? Can you bring me through the steps?
 
  • #4
dx
Homework Helper
Gold Member
2,011
18
It's a standard limit. Use the binomial theorem to expand (1 + (1/n))n, and then take the limit n → ∞. You should get

1 + 1 + 1/2! + 1/3! + ... = e
 

Related Threads for: Ratio Test

  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
687
  • Last Post
Replies
11
Views
685
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
823
  • Last Post
Replies
1
Views
942
  • Last Post
Replies
7
Views
782
  • Last Post
Replies
17
Views
3K
Top