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Trying to prove an inequality

  1. Oct 22, 2007 #1
    1. The problem statement, all variables and given/known data
    If 0 <= f(x) < infinity, then I need to show that e^x > (1 +f(x)/n)^n for x in (0, infinity)

    2. Relevant equations

    3. The attempt at a solution
    I'm pretty sure the answer lies in the comparison of the series representation for e^x and writing (1 +f(x)/n)^n out with the binomial theorem. I did so, however I still don't see it.
  2. jcsd
  3. Oct 22, 2007 #2
    Is this supposed to be true for all n, or the limit as approaches infinity or what? Suppose f(0)=1 then the statement is false for n=1, and x=0.
  4. Oct 22, 2007 #3
    for all n, and x > 0 though.
  5. Oct 23, 2007 #4
    Again take n=1, and any function f(x) such that f(1)=2, and it is false.
  6. Oct 23, 2007 #5
    Yea it must be a typo on my teachers part. I'm going to guess he meant e^f(x).
  7. Oct 23, 2007 #6
    Well in that case writing out the series expansions for both sides of the equation would help.
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