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!

Monotony of a recurrence relation

  1. Oct 21, 2014 #1
    What method should i use to know if a recurrence relation is increasing or decreasing?
    i was given the following relation:
    A1 = 1
    An=(An-1)^5 - 3

    I know for sure it actually decreases since every term for n>=2 is a negative number raised to and odd number, but i don't know how to demonstrate it mathematically. I tried using induction, but it doesn't work...

    Thanks to whoever can answer me.
     
  2. jcsd
  3. Oct 21, 2014 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Why do you think induction doesn't work?

    It's clear that if ##A_n < 0## then ##A_{n+1} < A_n## and that's your inductive step.
     
  4. Oct 21, 2014 #3

    pasmith

    User Avatar
    Homework Helper

    You can show that [itex]|A_n|[/itex] is strictly increasing. If all terms are negative this shows that [itex]A_n[/itex] is strictly decreasing. For [itex]n \geq 2[/itex] you have that [itex]|A_{n+1}| = |A_n^5 - 3| = |A_{n}|^5 + 3 > |A_n|^5[/itex]. If you can show that [itex]|A_{n}|^5 > |A_n|[/itex] you are done.
     
  5. Oct 21, 2014 #4
    Thanks guys, very quick and useful answers! I'll keep practising so i can see it by myself next time!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Monotony of a recurrence relation
  1. Recurrence Relation (Replies: 11)

  2. Recurrence relation (Replies: 7)

  3. Recurrence relation (Replies: 6)

  4. A recurrence relation (Replies: 7)

Loading...