Can we say that ?
(with being the Golden Ratio)
Which gives us the confirmed infinite fraction
We also have
So by analogy we can deduce that
The sequence such that gives , so indeed the representation should be correct.
Everywhere on the Internet that I see a continued fraction of , it is
Why haven't I seen the representation mentioned, and see the above used instead? Is something wrong about my representation?
I would say it isn't mentioned because it is not useful: you cannot approximate using the representation, unlike you can using the above one (which you can do by removing n any member).