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Prove sequence is increasing

  1. Oct 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Let b1=1 and bn=1+[1/(1+bn-1)] for all n≥2. Note that bn≥1 for all n in N (set of all positive integers).



    3. The attempt at a solution

    Prove that (b2k-1)k in N

    By definition, a sequence (an) is increasing if an≤an+1 for all n in N.

    SO, for this problem, must prove b2n-1≤b2n for all n.

    Proceed by induction:

    Start with n=1.
    Then,
    b1=1 and b2=3/2, so
    b1≤b2.

    Assume inductively that b2n-1≤b2n, prove b2n≤b2n+1

    Am I doing this correctly? I want to know before I continue.

    Thanks.
     
    Last edited: Oct 13, 2012
  2. jcsd
  3. Oct 13, 2012 #2

    Zondrina

    User Avatar
    Homework Helper

    Yes, induction is indeed appropriate here.

    Hmm, you could have also treated your sequences like functions and used the first derivative test :)
     
  4. Oct 13, 2012 #3
    Edit: I made a mistake, it's prove b2n-1≤b2n+1
     
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