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HELP how to prove (1-x^2)^n >= 1-nx^2 when x belongs to the interval [-1,1]?

  1. Jul 21, 2011 #1
    i got this question when i read the proof of stone-weierstrass theorem in baby rudin , page 159 , this inequality seems right when n becomes larger, since 1-nx^2 would be negative and (1-x^2)^n always positive, but i don't know how to proved it rigorously using binomial theorem for all n , or is there any other rigorous proof ?
     
  2. jcsd
  3. Jul 21, 2011 #2
    look up Bernoulli's inequality
     
  4. Jul 21, 2011 #3

    micromass

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    Try induction.

    A more general inequality is called Bernouilli's inequality and states that
    [tex](1+x)^n\geq 1+nx[/tex]
    for [itex]x\geq -1[/itex] and [itex]n\geq 1[/itex]. See http://en.wikipedia.org/wiki/Bernoulli's_inequality
     
  5. Jul 21, 2011 #4
    many thanks for your help~
     
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