# Another math question

**URL:** <https://forum.kirupa.com/t/another-math-question/6584>\
**Category:** Uncategorized\
**Created:** [October 10, 2002, 11:44pm UTC](https://forum.kirupa.com/t/another-math-question/6584 "2002-10-10T23:44:08Z")\
**Posts on this page:** 9\
**Page:** 1

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**Author:** ![sbeener](https://yyz1.discourse-cdn.com/flex011/user_avatar/forum.kirupa.com/sbeener/32/75_2.png) [@sbeener](https://forum.kirupa.com/u/sbeener)\
**Post date:** [October 10, 2002, 11:44pm UTC](https://forum.kirupa.com/t/another-math-question/6584/1 "2002-10-10T23:44:08Z")

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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?

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**Author:** ![system](https://canada1.discourse-cdn.com/flex011/uploads/kirupa/original/3X/6/2/621e5c11736f46532526e61be85940af4230f3e5.png) [@system](https://forum.kirupa.com/u/system)\
**Post date:** [October 15, 2002, 5:04am UTC](https://forum.kirupa.com/t/another-math-question/6584/2 "2002-10-15T05:04:26Z")

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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.

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**Author:** ![system](https://canada1.discourse-cdn.com/flex011/uploads/kirupa/original/3X/6/2/621e5c11736f46532526e61be85940af4230f3e5.png) [@system](https://forum.kirupa.com/u/system)\
**Post date:** [October 15, 2002, 5:14am UTC](https://forum.kirupa.com/t/another-math-question/6584/3 "2002-10-15T05:14:44Z")

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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:

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**Author:** ![system](https://canada1.discourse-cdn.com/flex011/uploads/kirupa/original/3X/6/2/621e5c11736f46532526e61be85940af4230f3e5.png) [@system](https://forum.kirupa.com/u/system)\
**Post date:** [October 15, 2002, 5:39am UTC](https://forum.kirupa.com/t/another-math-question/6584/4 "2002-10-15T05:39:10Z")

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_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:

```auto

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

```

the equation you wrote above looks strikingly similiar.

however, isolating x is still eluding me.

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**Author:** ![system](https://canada1.discourse-cdn.com/flex011/uploads/kirupa/original/3X/6/2/621e5c11736f46532526e61be85940af4230f3e5.png) [@system](https://forum.kirupa.com/u/system)\
**Post date:** [October 15, 2002, 5:42am UTC](https://forum.kirupa.com/t/another-math-question/6584/5 "2002-10-15T05:42:41Z")

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

pom :asian:

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**Author:** ![system](https://canada1.discourse-cdn.com/flex011/uploads/kirupa/original/3X/6/2/621e5c11736f46532526e61be85940af4230f3e5.png) [@system](https://forum.kirupa.com/u/system)\
**Post date:** [October 15, 2002, 5:47am UTC](https://forum.kirupa.com/t/another-math-question/6584/6 "2002-10-15T05:47:58Z")

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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?

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**Author:** ![system](https://canada1.discourse-cdn.com/flex011/uploads/kirupa/original/3X/6/2/621e5c11736f46532526e61be85940af4230f3e5.png) [@system](https://forum.kirupa.com/u/system)\
**Post date:** [October 15, 2002, 5:56am UTC](https://forum.kirupa.com/t/another-math-question/6584/7 "2002-10-15T05:56:49Z")

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almost.

in:

x + x^1 + x^2 … + x^n = d

given n and d, what is x?

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**Author:** ![system](https://canada1.discourse-cdn.com/flex011/uploads/kirupa/original/3X/6/2/621e5c11736f46532526e61be85940af4230f3e5.png) [@system](https://forum.kirupa.com/u/system)\
**Post date:** [October 15, 2002, 6:20am UTC](https://forum.kirupa.com/t/another-math-question/6584/8 "2002-10-15T06:20:47Z")

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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.

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**Author:** ![system](https://canada1.discourse-cdn.com/flex011/uploads/kirupa/original/3X/6/2/621e5c11736f46532526e61be85940af4230f3e5.png) [@system](https://forum.kirupa.com/u/system)\
**Post date:** [October 15, 2002, 6:24am UTC](https://forum.kirupa.com/t/another-math-question/6584/9 "2002-10-15T06:24:41Z")

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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 😏