Question

Is there any known geometric progression, construction, that generates ((x+1)^n)/(x^n) [((x+1}^n)*(x^-n)] for n=1 to infinity?

Answer 1

\[ \frac 1{1-x} = \sum_{n=0}^\infty x^n , |x|<1\]

Answer 2

Is that a geometric construction (progression)?

Answer 3

yes ... the left side is called generating function.