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 $1-$.
Asked
Active
Viewed 43 times
2 Answers
2
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$$a(1+b)(1+b+b^2+b^3+\cdots).$$
José Carlos Santos
- 427,504
-
So $a + (1+b)+$ geometric series? – Rory McEwan May 30 '18 at 08:41
-
I rather think that the expression reads $a\dfrac{1+b}{1-b}$. – May 30 '18 at 08:42
-
@YvesDaoust I think you're right – Rory McEwan May 30 '18 at 08:43
-
@YvesDaoust Right. I've edited my answer. – José Carlos Santos May 30 '18 at 08:46
-
@calcstudent No. It is $a+(1+b)\times$ a geometric series. – José Carlos Santos May 30 '18 at 08:46
0
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.