# Math Help - Binomial Theorem and Squeeze Theorem to Compute Limit

1. ## Binomial Theorem and Squeeze Theorem to Compute Limit

Question: Use the Binomial Theorem and Squeeze Theorem to compute lim(1+(1/n^2))^n as n goes to infinity.

I used direct substitution using the binomial theorem, but can't seem to get very far. Any ideas?

2. ## Re: Binomial Theorem and Squeeze Theorem to Compute Limit

I would rewrite the expression as follows:

$\left(1+\frac{1}{n^2} \right)^n=\left(\frac{n^2+1}{n^2} \right)^n=\frac{\left(n^2+1 \right)^n}{n^{2n}}$

Now, you need to find functions $f(n)$ and $g(n)$ such that:

$f(n)\le\left(n^2+1 \right)^n\le g(n)$

and where:

$\lim_{n\to\infty}\frac{f(n)}{n^{2n}}= \lim_{n\to\infty}\frac{g(n)}{n^{2n}}$

Can you find such functions?