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!

Homework Help: 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.
    b1=1 and b2=3/2, so

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

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

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


    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook