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February 21st, 2019, 02:20 PM   #1
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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 08:22 PM.
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February 21st, 2019, 10:00 PM   #2
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0.697774657964... (see this W|A link)
Thanks from topsquark and SenatorArmstrong
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February 22nd, 2019, 02:41 PM   #3
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How did you prove it?

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Originally Posted by skipjack View Post
0.697774657964... (see this W|A link)
How did you prove it?
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February 22nd, 2019, 09:14 PM   #4
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I didn't prove it. I just used Google.
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March 3rd, 2019, 08:32 PM   #5
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I didn't prove it. I just used google.
Prove it.

Last edited by skipjack; March 19th, 2019 at 06:20 PM.
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