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# e

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Euler''s e is approx 2.18~~~~ I know that it you get closer and closer to it when (1+(1/n))^nt -> t increases. But what''s the exact equation that leads you to e?
Charles Hwang -aka oatmeal.net [Maxedge My Site(UC)|E-mail|NeXe|NeHe|SDL] [Google|Dev-C++|GDArticles|C++.com|MSDN]

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Everything you''ve always wanted to know about e but were afraid to ask: http://mathworld.wolfram.com/e.html

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AHH! *Brain Explodes* Is there a version of the answer which an 8th grader could understand?

Charles Hwang -aka oatmeal.net
[Maxedge My Site(UC)|E-mail|NeXe|NeHe|SDL]

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e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + 1/6! ... ... ...

When I was in 8th grade, I didn''t know what x! meant, so incase you''re like me...

x! = x*(x-1)(x-2)(1)

So 5! = 5*4*3*2*1
8! = 8*7*6*5*4*3*2*1

Hope that helps explain.

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If the ... means it continues on forever, how do you get a single definite irrational number?

Charles Hwang -aka oatmeal.net
[Maxedge My Site(UC)|E-mail|NeXe|NeHe|SDL]

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quote:
Original post by Skybin
If the ... means it continues on forever, how do you get a single definite irrational number?

What do you mean by definite irrational number? Irrational numbers are approximations. As carry the series representing the value out to greater iterations, you get better approximations. Just like sin, cos, tan, pi, etc..

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By it''s very definition, you cannot express an irrational number as a decimal. Any decimal representation is therefore an approximation.

e, pi, sqrt(2), are all irrational numbers. The formulas you will find for them will only ever give approximations if you try to evaluate them.

- Xavier

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I think he''s looking for an equation like the famous PI equation that gives you a hexadecimal digit of pi for each n you plug in.

However, as an 8th grader myself, I don''t know it.

<-- that''s still a link if you didn''t notice
"Gay marriage will encourage people to be gay, in the same way that hanging around tall people will make you tall." - Grizwald

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The infinite series is an ok way to approximate e. Using 6 terms gives you 3 digits of accuracy.

The equation you mentioned, (1 + 1/x)x x->∞ is one of the definitions of e. In other words, that is an equation that leads you to the exact value of e. On Mathworld there are several other formulas that are identities of e but they generally involve some trigonometric function or hyperbolic functions.

"I forgot I had the Scroll Lock key until a few weeks ago when some asshole program used it. It even used it right" - Conner McCloud

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The definition I like best is d/dx(e^x) = e^x, i.e. y=e^x has a gradient of e^x.
Using that you can obtain the series Kranar gave with a little bit of brain work.

[edited by - furby100 on May 7, 2004 4:40:54 PM]

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