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.

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- Jul 17th 2007, 07:36 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, 07:58 AMgalactus
Try using the fact that

Your problem is a variation on a theme. - Jul 17th 2007, 07:58 AMred_dog
The sequence converges to when

- Jul 17th 2007, 08:53 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, 10:08 AMred_dog

- Jul 17th 2007, 10:09 AMCaptainBlack
- Jul 17th 2007, 10:39 AMCaptainBlack
- Jul 17th 2007, 10:54 AMThePerfectHacker
You can use this.

- Jul 17th 2007, 11:33 AMgalactus
Here's a fairly simple proof I just scratched down.

Let