The task is to show why e^2x = (1+2x/n)^n for very large n. I'm not sure how to tackle this problem. I thought about creating the generating functions and doing some algebraic manipulation but couldn't finish it.

Printable View

- Jul 17th 2007, 08:36 AMCrazyAsiane^2x = (1+2x/n)^n for large n?
The task is to show why e^2x = (1+2x/n)^n for very large n. I'm not sure how to tackle this problem. I thought about creating the generating functions and doing some algebraic manipulation but couldn't finish it.

- Jul 17th 2007, 08:58 AMgalactus
Try using the fact that

Your problem is a variation on a theme. - Jul 17th 2007, 08:58 AMred_dog
The sequence converges to when

- Jul 17th 2007, 09:53 AMCrazyAsianThanks but...
I don't think that's the method they are looking for because the next question is proving:

E^(-x^2/2) = Cos[x/(n^0.5)]^n as n approaches infinity. - Jul 17th 2007, 11:08 AMred_dog

- Jul 17th 2007, 11:09 AMCaptainBlack
- Jul 17th 2007, 11:39 AMCaptainBlack
- Jul 17th 2007, 11:54 AMThePerfectHacker
You can use this.

- Jul 17th 2007, 12:33 PMgalactus
Here's a fairly simple proof I just scratched down.

Let