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What number has this continued fraction: [5, 10, 10, 10, 10.........etc]?. Thanks for help.

 Dec 18, 2018
 #1
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+1

Here a very short computer code to calculate it for you:
c=1E100; listforeach(b,reverse(5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10), c=b + 1/c);printc
c=5.0990195135 9278483002 8224^2 =26. So, the continued fraction is the square root of 26.

 Dec 18, 2018
 #2
avatar+94526 
+2

This will result in an irrational number

 

10 + 1/10 =  11/10

10 + 10/11 = 120/11

10 + 11/120 = 1211/120

10 + 120/1211 = 12230/1211

 

5 + 1211/12230 ≈  5.099....   =  √26

 

 

cool cool cool

 Dec 18, 2018

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