I think that maybe I am missing that mathematically fundamental here which I cannot figure it out or the following is completely wrong.
I saw somewhere this one :
$$ g(x_{i})=\frac{\sum_{i=1}^{n}(x_{i,j}^{2}\times \theta^{n-i})}{\sum_{i=1}^{n}\theta^{n-i}} $$ where $x$ is a vector (probably multivariate),$n=10$ and $\theta >0$ constant. I think that the term $\sum_{i=1}^{n}\theta^{n-i}$ cancels out.In order now to cancel out it must be zero.Or because it is inside a sum must be kept ? Any help ?