So, here's the motivation to my problem:(adsbygoogle = window.adsbygoogle || []).push({});

I have this following equation:

[tex]P(u) = \frac{u^n}{1+u+u^2+...+u^n}[/tex]

, 'n' being a given constant.

I figured out that I could simplify the power series on the denominator, and get a better solution for P(u):

[tex]P(u) = \frac{u^n-u^{n+1}}{1 - u^{n+1}}[/tex]

Now, I am interested in P(u) = x, and 'x' is a number between 0 and 1.

What I have been struggling with is finding an analytical solution for u(x).

To make it more clear, I would like to know what 'u' will equal, for a given 'x' value, and a known 'n'.

I've tried a lot of different approaches, but I just can't seem to come up with an analytical solution for u(x).

One attempt and where I get stuck: [tex]u^n + u^{n+1}(x-1) = x[/tex]

Any help would be appreciated. I would like to be enlightened. =p

Thanks,

Mark

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# Help: want to find an analytical soln to this =p

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