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Maximizing a summation without equals its derivation to zero

  1. Jul 20, 2011 #1
    Hi,
    I have sent the following question a couple of days ago. I want to ask my question in a more

    general way; Could you please guide me if we have some ways to find the maximum value of a

    summation without getting derivation and equals it to zero?

    My problem:What is the maximum value of the given summation in terms of [itex]k, l

    [/itex] and [itex]N[/itex] ?
    [tex]max_{0\leq x \leq k} \sum_{(l_1,l_2)\in A} \frac{N!}{(N-l_1-l_2)!l_1!l_2!} x^{l_1}(k-

    x)^{l_2}(1-k)^{N-l_1-l_2}[/tex]
    where [itex]A=\{l_1,l_2 \in \{0,1,...,N\}|l_1+2l_2=l, l_1+l_2\leq N \}[/itex]. Also, [itex]l \in \{0,1,...,2N \}[/itex] and [itex]0<k<1[/itex].


    Thanks a lot for your participation.
     
    Last edited: Jul 20, 2011
  2. jcsd
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