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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

summationwithout 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.

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# Maximizing a summation without equals its derivation to zero

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