Integer Partitions asymptotic behaviour Let $ P(n) $ be the number of partitions of number $n$. 
Prove that $ P(n)$, grows faster than any polynomial from $n$.
I am looking for an elementary (rather bijective) proof of the fact.

If $P(n,k)$ is the number of partitions of $n$ into at most $k$ parts, then
$$\sum_{n=0}^\infty P(n,k)t^n=\frac1{(1-t)(1-t^2)\cdots(1-t^k)}.$$
(If $P(n,k)$ is the number of partitions of $n$ into at exactly $k$ parts, then the generating function is $t^k$ times this.)
This has a partial fraction expansion as a linear combination of
terms of the form $1/(1-\zeta t)^m$ where $\zeta$ is a root of unity
and $m$ is a positive integer. The dominant contribution to the
generating function will come from the term involving $1/(1-t)^k$.
