Is this in the form of a geometric series?

Question

Is the equation below a geometric series? I think yes but the only thing that bothers me is the $1+$ in the numerator. I think it would usually be $1-$.

Answer 1

This is not a series. It is a rational expression of the type $a\frac{1+b}{1-b}$. If $|b|<1$, then it can be expressed as the sum of$$a(1+b)(1+b+b^2+b^3+\cdots).$$

Answer 2

You can "see" a geometric progression in any number $r$, as

$$r=\frac1{1-s}=1+s+s^2+s^3+s^4+\cdots$$ where $s=1-\dfrac1r$ (provided $r>\frac12$; but you can rescale).

So your statement is a little artificial.