1. Limited time only! Sign up for a free 30min personal 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!

Sequences- help, please!

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data

    For the sequence (see picture), explore its monotones, define supermum and infimum, minimum and maximum, and find if the sequence is convergent. If the sequence is convergent, find form where on the terms of this sequence differ from the limit for less than ε = 0.01.

    3. The attempt at a solution

    a1= 1
    a2= 1/4
    a3= 1/9
    a4= 1/16
    a5= 1/25

    Concussion: the sequence is decreasing.

    Prove:
    a(n+1) ≤ an
    (1/n+1)^n ≤ (1/n)^n
    (1/n+1)^n – (1/n)^n ≤ 0

    Since (1/n+1)^n will always be smaller than (1/n)^n, I concluded that the left side will always be smaller than 0. I think this is the prove that the sequence is decreasing.

    Now, I stuck. How do you know if the the sequence is monotonic, how can I define supermum and infimum, min and max? And how can I prove if it is convergent or not?
     

    Attached Files:

  2. jcsd
  3. Oct 17, 2009 #2
    From the terms you give, your sequence appears to be (1/n)2, not (1/n)n. The argument you gave in your limit has to be adjusted for this.
     
  4. Oct 17, 2009 #3
    Ooops, my bad. It was a typo. It should be like this:

    a1= 1
    a2= 1/4
    a3= 1/27
    a4= 1/256
    a5= 1/3125
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook