Partition

For positive integer $n$ , let $f(n)$ represent the number of distinct ways of representing $n$ as a sum of positive integers.

For example $f(4)=5$ because $4$ can be written as $1+1+1+1=1+1+2=1+3=2+2=4$ .

Find $\displaystyle \lim_{n\to\infty}\dfrac{\ln\left(f(n)\right)}{\sqrt{n}}$