another math question

[sbeener]

ok,

boy math 12 feels like a long time ago now...

x^1 + x^2 + x^3 + x^4 = d

given d, how can i solve for x?

[Capn]

I thought I had this figured out until I realized I had calculateed for
x^1 + x^2 + x^3 + x^4 +.... x^n = d

I'll give you the solution for that anyway, maybe it will help.

The above formula can be broken down to:
x
------- = d
1 - x

which works out to become:

d
--- = 1 + d
x
and then:

d
--- = x
1-d


However, this only works with the equation continuing to x^n. Assuming x<1, the value of x gets smaller and smaller as it approaches the value of d. It's essentially a probability equation.

I hope this helps you out a bit, I'll see if I can figure out the answer to your exact question, but maybe you'll be able to figure it out after seeing this one.

[pom]

Well, Supra, there is no simple way (that I know of) to calculate the root of a polynom of the 4th degree (that's what we call them in France....).
Degree 2: easy
Degree 3: very tricky techniques
Degree 4: I don't think you can do that, unless it is a very simple one.

The above formula can be broken down to:
x
------- = d
1 - x
You're sure about that? What about x=1?

pom :cowboy:

[sbeener]

whoops, edited to fix total screwup

thanks,

to the n degree is actually exactly what i'm looking for.

further research (http://www.math.ubc.ca/~cass/courses/m102/text/exp.pdf) revealed the following equation:

1 - x^n
d = -----
1 - x

the equation you wrote above looks strikingly similiar.

however, isolating x is still eluding me.

[pom]

This is only true if x<1. Otherwise, it will not converge to that limit. It will not converge at all, actually.

pom :asian:

[pom]

OK, so you're looking for the solution of

x^1 + x^2 + x^3 + x^4 +.... x^n = d

with x < 1 and n -> infinity. Is that right?

[sbeener]

almost.

in:

x + x^1 + x^2 ... + x^n = d

given n and d, what is x?

[Capn]

I did verify that x<1, reread my post if you didn't catch it the first time, ilyaslamasse (pom).
"...x<1, the value of x gets smaller and smaller..."

But anyway, the math is bogging me down. I'll see if I can think of an answer tomorrow, with n and d defined, since my formula assumes n approaches infinity.

[pom]

Oups sorry. I guess I was confused because I was thinking about a general solution to the equation. I'll do my little research too :)

pom :smirk: