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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
    b^n-a^n<(b-a)n*b^(n-1)
    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

    morphism

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    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!
     
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