Question 141
For a positive integer $n$, let $p(n)$ denote the number of sequences of positive integers the sum of whose terms is equal to $n$. Show that
$$
\frac{1 + p(1) + p(2) + \dots + p(n-1)}{p(n)} \le \sqrt{2n} .
$$
$$
\frac{1 + p(1) + p(2) + \dots + p(n-1)}{p(n)} \le \sqrt{2n} .
$$