Mosca
Mosca
Joined: Dec 14, 2009
  • Threads: 181
  • Posts: 3833
November 17th, 2021 at 7:59:28 AM permalink
I知 interested in the answer, but I知 more interested in the method for how to approach this. In the middle of a dream last night I thought of this number:



And in the dream I was trying to figure out what number it was. I knew (in the dream) that it approached a limit, but since I was dreaming it just turned into one of those circular dreams where I kept getting dumped to the beginning.

It looks like it痴 just a tick over 1/2, but how do I think about it to find out what it really is?
NO KILL I
ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
  • Threads: 106
  • Posts: 5072
Thanks for this post from:
Mosca
November 17th, 2021 at 8:02:54 AM permalink
An easy one...

Let X = 1 / (1 + 1 / (1 + 1 / (1 + 1 / (....)

1 / X = 1 + 1 / (1 + 1 / (1 + 1 / (....)
1 / X - 1 = 1 / (1 + 1 / (1 + 1 / (....) = X
X - 1 / X + 1 = 0
X^2 + X - 1 = 0
X = -1/2 +/- sqrt(5)/2
but in this case, X > 0, so X = (sqrt(5) - 1) / 2
Mosca
Mosca
Joined: Dec 14, 2009
  • Threads: 181
  • Posts: 3833
November 17th, 2021 at 8:07:55 AM permalink
Quote: ThatDonGuy

An easy one...

Let X = 1 / (1 + 1 / (1 + 1 / (1 + 1 / (....)

1 / X = 1 + 1 / (1 + 1 / (1 + 1 / (....)
1 / X - 1 = 1 / (1 + 1 / (1 + 1 / (....) = X
X - 1 / X + 1 = 0
X^2 + X - 1 = 0
X = -1/2 +/- sqrt(5)/2
but in this case, X > 0, so X = (sqrt(5) - 1) / 2
link to original post



Thanks, ThatDonGuy! I don稚 algebra much, so I had to write that down and look at it as I did it. But I got it. The method is what I was looking for. Dreams are strange.
NO KILL I

  • Jump to: