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About e

  1. Jan 27, 2008 #1
    the quesion is below, show that
    show that ( 1+ [tex]\frac{x}{n}[/tex] ) ^n < e^x

    at the first, i take log on both sides,.. but i couldn't go further.

    can someboday help me?

    thx
     
  2. jcsd
  3. Jan 27, 2008 #2

    EnumaElish

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    What do you get when you apply log to both sides?
     
  4. Jan 27, 2008 #3

    mathman

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    Expand the lhs by the binomial theorem and take the power series for e^x. The solution becomes obvious for x>0. For x<0, it is a little trickier - work with terms 2 at a time.
     
    Last edited: Jan 27, 2008
  5. Jan 27, 2008 #4
    thx so much
     
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