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Math Help - Summation Problem

  1. #1
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    Summation Problem

    Hi,

    Can anyone please help me on how to solve for p in terms of n and k in the following equation?

    Summation Problem-untitled.jpg

    Thank you.

    Regards
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  2. #2
    Moo
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    Hello,

    Why do you need this ? Is it a probability based question ? Is it the real wording of the question ?

    Because as far as I can see, there are multiple solutions
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  3. #3
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    Hi,

    It is not exactly a probability question. This is part of my research where I need to find the intersection of the 2 curves for 0<p<1 given a fixed n and k. I am not majoring in mathematics and hence am having problems with solving it.

    Summation Problem-untitled.jpg

    I don't think that there are multiple solutions as you have pointed out. In particular, (1) is monotonically increasing while (2) is a lateral reflection of it which is monotonically decreasing. So there must a a unique p that solves it.

    By the way, I suspect that p=(k-1)/(n-1) from a series of graphs I have plotted but just can seem to prove it analytically.
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