First: I will be appreciated if you do the the expansion of $$ \frac{x}{1-x-x^2}$$ Second: I've seen in some textbook(generatingfunctionology) in a phase of exapnsion it told: $$\frac{1}{1-xr_+}=\sum_{j=0}^\infty x^j+r^j$$ I was confused when I saw the following in wikipedia: $$\sum_{n=0}^\infty (rx)^n=\frac{1}{1-xr}$$ (For your information$$ r_+=\frac{\sqrt{5}+1}{2}$$) Now I don't know how those two sum are equal and how do thay Measured the first sum .
Asked
Active
Viewed 30 times
0
-
Welcome to the community! It seems that in the textbook the sign is misprinted as $+$ and it should be $x^j × r^j$ – Ѕᴀᴀᴅ Jan 22 '18 at 08:00
-
Thanks.which one of them? – Abbas Jan 22 '18 at 08:02
-
Thanks again but what is the proof of $$ \sum_{n=0}^\infty (rx)^n =\frac{1}{1-xr}$$ – Abbas Jan 22 '18 at 08:13
-
@Abbas The proof of that is the Geometric Series. Start googling it, and read some wikipedia notes. – Enrico M. Jan 22 '18 at 08:23
-
Thank you for answering – Abbas Jan 22 '18 at 14:40