I am looking to try and formulate a simple proof of the result obtained from Wick's Theorem used in the context of Brownian Motion, specifically
$\mathbf{E}[B(t_1)B(t_2)...B(t_{2k-1})] = 0$, $\\$ and, $\mathbf{E}[B(t_1)B(t_2)...B(t_{2k})] = (2k-1)!!t^k$.
I currently am a little lost as to how to go about working this problem and would appreciate any help that anyone can offer!