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Discrete Math Proof

  1. Jan 15, 2013 #1
    1. The problem statement, all variables and given/known data
    http://puu.sh/1OfE2 [Broken]


    2. Relevant equations



    3. The attempt at a solution
    I am not really sure about this one! :(
    I think it's 1 because
    http://puu.sh/1OfY0 [Broken]
    http://puu.sh/1OfYE [Broken]

    I came up the number by working backwards (assuming the conclusion is true). However, for a proof, I cannot assume the conclusion is true and try proving the hypothesis. Could someone nudge me to the right direction in proving this statement?

    Thanks!
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 16, 2013 #2

    CompuChip

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    As you say,
    [tex]\lim_{x \to \infty} 2^{\frac{1}{x}} = 1[/tex]
    But since this is discrete mathematics, perhaps it's more intuitive to define an = 21/n and write
    [tex]\lim_{n \to \infty} a_n = 1[/tex]

    Now can you solve it if I say: "[itex]r = 1 + \epsilon[/itex]" and "definition of limit"?
     
  4. Jan 16, 2013 #3
    No, I don't understand the second part with epsilon.
     
  5. Jan 16, 2013 #4

    CompuChip

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    Do you know what the definition of the limit is?
     
  6. Jan 16, 2013 #5

    lurflurf

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    Consider n<0
     
  7. Jan 16, 2013 #6
    When I graphed it, i found out that r > 0.5 because 2^(-1) is 0.5 since n has to be int and -1 is an int but i don't know how to prove it. Graphing is not a good way, according to my Prof.
     
  8. Jan 16, 2013 #7

    CompuChip

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    If you haven't learned the definition of limit yet, another approach is as follows: try solving the equation 2^(1/x) = r first. Once you find x for which the equality holds, you can may use your graph for inspiration for an integer n such that the inequality holds.
     
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