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February 21st, 2019, 01:20 PM  #1 
Newbie Joined: Feb 2019 From: San Diego, CA Posts: 3 Thanks: 0 Math Focus: Everything  1/(1+1/(2+1/(3+1/(4+1/(5+1/...)))))
What is the following expression's value? $\displaystyle \frac{1}{1 + \frac{1}{2 + \frac{1}{3 + \frac{1}{4 + \frac{1}{5 + \frac{1}{...}}}}}}$ Last edited by skipjack; February 21st, 2019 at 07:22 PM. 
February 21st, 2019, 09:00 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,485 Thanks: 2041 
0.697774657964... (see this WA link)

February 22nd, 2019, 01:41 PM  #3  
Newbie Joined: Feb 2019 From: San Diego, CA Posts: 3 Thanks: 0 Math Focus: Everything  How did you prove it? Quote:
 
February 22nd, 2019, 08:14 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,485 Thanks: 2041 
I didn't prove it. I just used Google.

March 3rd, 2019, 07:32 PM  #5 
Newbie Joined: Feb 2019 From: San Diego, CA Posts: 3 Thanks: 0 Math Focus: Everything  Last edited by skipjack; March 19th, 2019 at 05:20 PM. 