1/e hmmmm..... simple?

[Sarahisme]

Hi all again!

 

I'm sure there is a simple answer/solution to this problem...or a way to do it anyway, i just can't seem to get it.

 

why does this = 1/e?

 

Thanks

 

Sarah

[Yggdrasil]

Look up the definition of e, for example at Wikipedia:

 

http://en.wikipedia.org/wiki/E_%28mathematical_constant%29

[Sarahisme]

oh lol, so its just by definition ?

[matt grime]

it depends on what you take as your definiton of exp(x) i suppose, but it is a standard exercise in anaylsis to demonstrate that (1+1/n)^n converges to e (where we define e in some other equivalent way), and not too hard if you are familiar with analysis.

[Dave]

In the analysis course I took, we started with the familiar Taylor series of exp at 1:

 

[math]e = 1+ 1 + \frac{1}{2!} + \frac{1}{3!} + \cdots[/math]

 

We then went on to prove that the limit converges to this. It's not particularly hard, and I'm sure that most other Analysis courses approach it in a similar style.

 

Edit: Just noticed matt's post makes it a little redundant, but never mind.