"e" Natural Base

[NSX]

Just a little food for thought kinda thread here; what ways are there to find the numerical value of "e", that is, the natural base.

 

There's 2 I learned this semester:

1. 1/1! + 2/2! + 3/3! + ... n/n!, as n-->infinity where n is an element of natural numbers

Or something like that

 

and

 

2. The fundamental limit of calculus, that is:

lim x-->infinity for (1 + 1/x)^x

[JaKiri]

It's e = 1/0! + 1/1! + 1/2! + 1/3! (etc), which is something called a Taylor series; you get a good value out pretty quickly too.

[NSX]

Originally posted by MrL_JaKiri

It's e = 1/0! + 1/1! + 1/2! + 1/3! (etc), which is something called a Taylor series; you get a good value out pretty quickly too.

Yeah; something like that...lol

 

That's the taylor series eh?

I see; I hear you math gurus talking about it alot; where else do you use this taylor series?

[JaKiri]

A taylor series assumes you can express a function as an infinite sum of the differations of the function, basically.

[Dave]

It's very useful for proving things like Euler's formula (e^(pi * i) +1 = 0) and stuff like that. Not sure I can think of anything else to use it for, but it's mainly used in proofs and such things. And approximations to things like circular/hyperbolic functions etc.

[NSX]

Originally posted by MrL_JaKiri

A taylor series assumes you can express a function as an infinite sum of the differations of the function, basically.

 

WHat do you mean by differations?

[JaKiri]

Originally posted by NSX

 

WHat do you mean by differations?

 

+en.

 

Typographical error.

[NSX]

So are there any other ways to express "e"?

[NSX]

Originally posted by dave

It's very useful for proving things like Euler's formula (e^(pi * i) +1 = 0) and stuff like that. Not sure I can think of anything else to use it for, but it's mainly used in proofs and such things. And approximations to things like circular/hyperbolic functions etc.

 

What's the value of i?

i^2=-1, so that makes i

[fafalone]

i is defined as the square root of -1, thats it.

[JaKiri]

Originally posted by NSX

 

What's the value of i?

i^2=-1, so that makes i

 

i is the square root of minus 1.

 

It's just a number.

[NSX]

Originally posted by MrL_JaKiri

 

i is the square root of minus 1.

 

It's just a number.

 

Ah..darn;

hehe

I wanted to just plug it into my calculator and try it.