- #1
mkkrnfoo85
- 50
- 0
So, here's the motivation to my problem:
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
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
Last edited: