Halllo
I need to proove (in a formal way) in a formal way that when n=>infinity, lim (n^n)/((n!)^2)=0
if someone can hekp i would relly appriciate it...
Omri
let $\displaystyle a_n=\frac{n^n}{(n!)^2}.$ then: $\displaystyle \frac{a_{n+1}}{a_n}=\frac{1}{n+1} \left(1 + \frac{1}{n} \right)^n.$ thus: $\displaystyle \lim_{n\to\infty} \frac{a_{n+1}}{a_n} = 0 < 1.$ hence $\displaystyle \sum a_n$ is convergent. so: $\displaystyle \lim_{n\to\infty}a_n=0. \ \ \ \square$