Hi there. I (and the rest of the class) have been hitting the wall with this one for days. Would love if someone here can help us with this.
The problem's is this:
Thank you so much.
BTW:
Bernoulli's inequality:
Thanks again.
The problem's is this:
Now I've managed to prove x^2 is greater than the expression for large n, but no matter what permutation's of the expression I use Bernoulli's inequality with, I still don't get anything whose limit is x^2. Can anyone help?Prove the following:
n−>∞lim(2nx−1)n=x2
When x>1
Using the squeeze theorem and Bernoulli's inequality.
Thank you so much.
BTW:
Bernoulli's inequality:
Also, I can't use advanced calculus methods, like l'Hospital's rule and the such, because we haven't studied them, we're just on sequence limits for now, with sequence arithmetic and the such.For x>−1:
(1+x)n≥1+nx
Thanks again.