# The number e as a limit

1. Nov 29, 2015

### astrololo

1. The problem statement, all variables and given/known data
I have lim of n > infinity (1+1/n)^n

2. Relevant equations

3. The attempt at a solution
I know that I must use l'hospital rule and setting ln y = n ln (1+1/n)

And after lim n ln (1+1/n) as n approaches infinity.

After what do I do ?

2. Nov 29, 2015

### LCKurtz

Try writing it as$$\frac{\ln(1 + \frac 1 n)}{\frac 1 n}$$before using L'Hospital's rule and taking the limit.

3. Nov 29, 2015

### astrololo

OK but I'll have to take the natural logarithm right ?

4. Nov 29, 2015

### LCKurtz

Didn't you already take the logarithm to get that expression?

5. Nov 29, 2015

### Student100

You've either applied LH incorrectly, or I'm misreading you. How did you apply LH (how did you set it up) when you're at the step: $$exp[\lim_{n\to\infty}(n\log(1+\frac{1}{n})]$$

Never mind, didn't see the new post update. :) Ignore me LC's already said the same thing.

6. Nov 29, 2015

### astrololo

Wait, what I just wrote was correct or not ? Am I in the right direction ?

7. Nov 29, 2015

### LCKurtz

8. Nov 29, 2015

### Staff: Mentor

For this to work out correctly, you need to keep track of your equations. Each line you write should be an equation.
Let $y = (1 + 1/n)^n$
$\ln y = n \ln(1 + 1/n) = \frac{\ln(1 + 1/n)}{1/n}$
Now take limits of both sides, after which you can apply L'Hopital's Rule.

Again, take care to work with equations at each step.

9. Nov 29, 2015

### astrololo

I'm sorry if it takes time to respond, I have like several question to answer at the same and I must give this tomorrow lol Don't worry, I keep track of what I write on paper. I'll respond here if something I'm having a problem with.

10. Nov 29, 2015

### astrololo

Ok thanks it worked

11. Nov 29, 2015

### MidgetDwarf

Yes, but it is extremely rude and time consuming for the people on this site. How are we to know the work you present means.