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!

Proving r^n > r^m through mathematical induction

  1. Sep 20, 2011 #1
    1. The problem statement, all variables and given/known data

    I need to prove that for any real number r, if 0 < r < 1, then for all positive integers n and m, if n < m, then r^n > r^m.


    2. Relevant equations

    No calculus techniques are permitted, only mathematical induction.

    3. The attempt at a solution

    I know that any fraction between 0 and 1 is going to get smaller if it is multiplied by anything positive, so this is obviously true.

    I know that I first need to figure out what predicate to use, but I'm having a problem with all of the variables.

    Im not looking for the answer, just a little bit of direction. Where/how do I begin? I know what to prove, I just dont know how to prove it.

    Thanks for any help out there
     
  2. jcsd
  3. Sep 20, 2011 #2

    PeterO

    User Avatar
    Homework Helper

    Perhaps you could take the logarithm of both sides of the inequality.
     
  4. Sep 20, 2011 #3

    ElijahRockers

    User Avatar
    Gold Member

    To be honest I don't know much about induction, but it has been something I want to learn. I wasn't going to reply here because I don't know anything about it, but I went to khan academy and found this video! Coincidence? I don't know if it's what you need, but I hope it helps.

    http://www.khanacademy.org/video/proof-by-induction?playlist=Algebra
     
  5. Sep 20, 2011 #4

    uart

    User Avatar
    Science Advisor

    No, you have that the wrong way around. Anything positive is going to get smaller if multiplied by a number between 0 and 1. So that's the basis of your inductive step right there. Now you just need to write it out formally as an inductive proof.
     
    Last edited: Sep 20, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proving r^n > r^m through mathematical induction
Loading...