1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ratio Test

  1. May 31, 2009 #1
    1. The problem statement, all variables and given/known data
    http://img132.imageshack.us/img132/6663/captureqqi.jpg [Broken]

    2. Relevant equations



    3. 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: May 4, 2017
  2. jcsd
  3. May 31, 2009 #2

    dx

    User Avatar
    Homework Helper
    Gold Member

    (1 + (1/n))n → e (≈ 2.718) as n → ∞.
     
  4. Jun 1, 2009 #3
    How did you get that? Can you bring me through the steps?
     
  5. Jun 1, 2009 #4

    dx

    User Avatar
    Homework Helper
    Gold Member

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Ratio Test
  1. Ratio test. (Replies: 2)

  2. Ratio Test (Replies: 1)

  3. Ratio Test (Replies: 5)

Loading...