Homework Help: Maths project

1. Nov 6, 2008

seboastien

Maths project proving lim n-infinity (1+x/n)^n = exp(x)

1. The problem statement, all variables and given/known data
project aiming to show that limn→∞(1+x/n)^n = exp(x)

2. Relevant equations

3. The attempt at a solution
I have no Idea, is there any chance someone could give me some sort of clue?

Last edited: Nov 6, 2008
2. Nov 6, 2008

seboastien

here is my attempt so far,
(a+b)^n= (n) a^n + (n) a^n-1 b + (n) a^n-2 b^2 + ........... (n) b^n
(0) (1) (2) (n)

3. Nov 6, 2008

seboastien

I don't know what to do!!!
should I use (a+b)(a+b)^n-1?

4. Nov 6, 2008

bowma166

Try rewriting your limit as $$\lim_{n\rightarrow\infty}\exp\left[\ln\left(\left(1+\frac{x}{n}\right)^{n}\right)\right]$$.

From there, I believe, you should try to get it into a form where L'Hôpital's rule will apply.

edit :: Yup, I just worked it out and this works.

Last edited: Nov 6, 2008
5. Nov 7, 2008

morphism

How is exp(x) defined for you?

If it's defined as the inverse of the natural log, then bowma166's method is a good way to approach this problem. But be careful: first you must show that the limit

$$\lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n$$

exists, for all x.