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Monotonic 0<an<1 for all n and no two terms are the same

  1. Dec 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Give an example of a sequence {an}, satisfying the following:
    {an} is monotonic
    0<an<1 for all n and no two terms are the same
    lim(n→∞) an = 1/2

    2. Relevant equations
    what is monotonic


    3. The attempt at a solution
    1/(2√n)
    n/(2n-1)
    1/2^n

    just been trying genearal sequences but none of them work
     
  2. jcsd
  3. Dec 20, 2011 #2
    Re: sequence

    Does this one work?

    [tex] a_n = \frac{1}{2 } + \frac{1}{n}\ \forall n>2 [/tex]
     
  4. Dec 20, 2011 #3
    Re: sequence

    what would be the first term?
     
  5. Dec 20, 2011 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: sequence

    Oh, c'mon! Use any two numbers less than 1/2 for a1 and a2.
     
  6. Dec 20, 2011 #5
    Re: sequence

    monotonic refers to how it increases. monotonic increasing means each term is greater than or equal to the term before it. monotonic decreasing means each term is less than or equal to the term before it. if it just says monotonic, either situation will work.
     
  7. Dec 24, 2011 #6
    Re: sequence

    For all n
     
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