Let $\displaystyle f(x; \theta) = \theta^x (1- \theta)$. I need to find an unbiased estimator for theta.

$\displaystyle E(X) = \Sigma x \theta^x (1- \theta) = (1-\theta)\Sigma x \theta^x = (1-\theta) \frac{\theta}{(1-\theta)^2} = \frac{\theta}{1 - \theta}$.

Kinda stuck here. I tried to find $\displaystyle E(\frac{1}{X})$, but that didn't help either.

Any help would be appreciated.