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!

Where does this inequality come from?

  1. Sep 18, 2007 #1
    In Rudin's Principles of Mathematical Analysis, 3rd ed., I encountered the following on p. 10, and I'm not really sure where it comes from. I'll write it just as it is shown in the book.

    The identity
    b^n-a^n=(b-a)(b^(n-1)*a^0 + b^(n-2)*a^1 + ... + b^1*a^(n-2) + b^0*a^(n-1))
    yields the inequality
    when 0<a<b

    I understand where the indentity comes from. I'm just confused about the inequality, and I was curious. Thanks for sharing any ideas.
  2. jcsd
  3. Sep 18, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    0<a<b implies, for instance, that b^(n-2)a < b^(n-1). Do you see it now?
  4. Sep 18, 2007 #3
    Oh, of course. Thanks so much!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Where does this inequality come from?
  1. Where did pi come from? (Replies: 10)