So I'm supposed to prove that
And I'm doing so by using the squeezing theorem (with guided help from the book)
I know for certain that
(btw the left is 1 over e to the power of all that stuff, Latex is making it look weird)
This is correct. My book confirmed so. And I can see how the left side of the equation approaches 1/e. Somehow the right side does and I can't see how....anybody?
For the LaTeX code, you should wrap the whole 'power' in brackets like this:
e^{(1 - \frac{1}{n})}
As for the right side, 1/infinity tends to 0, and anything to the power of zero becomes 1.
So, you are left with:
Once again, 1/infinity tends to zero, and 1 + 0 = 1. So, you get 1/e.
I hope it helps!
Man, you guys replied fast, I was playing around with this for about 4 hours.
I'm trying to get better. Does anyone know of a book or source of really hard problems? I've found this:
http://www.maths.cam.ac.uk/undergrad...tep/advpcm.pdf
Any other sources?
When you have indeterminate limits (like in this case, ) you need to apply a transformation to get or so that you can then apply L'Hospital's Rule.
Indeterminate form - Wikipedia, the free encyclopedia