Here's the question you clicked on:
JerryP
Is there any known geometric progression, construction, that generates ((x+1)^n)/(x^n) [((x+1}^n)*(x^-n)] for n=1 to infinity?
\[ \frac 1{1-x} = \sum_{n=0}^\infty x^n , |x|<1\]
Is that a geometric construction (progression)?
yes ... the left side is called generating function.