Let $\{S(t), t\geq0\}$ a geometric brownian motion with drift $\mu$ and volatility $\sigma$. Find if the process is also a martingale or not.
I know that I have to prove that $$E[S(t)-S(t-1)\lvert S(t-1),S(t-2),\ldots,S(1),S(0)]=0$$ Or: $$E[S(t)\lvert S(t-1),S(t-2),\ldots,S(1),S(0)]=S(t-1)$$
But I really have no idea how to attack this problem, any suggestion is welcomed.