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This is the "continued fraction" of some irrational number. Can you figure out which irrational number is it? And to how many accurate decimal places can it be reconstructed from this continued fraction?

[3,7,15,1,292,1,1,1,2,1,3,1,…etc.]. Thanks for help.

Guest Apr 15, 2017
 #1
avatar+92856 
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[3,7,15,1,292,1,1,1,2,1,3,1,…etc.].

 

3 + 1/1  =  4

1 + 1/4   = 5/4

2 + 4/5   =  14/5

1 + 5/14  = 19/14

1+ 14/19 = 33/19

1 + 19/33   = 52/33

292 + 33/52  = 15217/52

1 + 52/15217 = 15269/15217

15 + 15217/15269  =  244252/15269

7 + 15269/244252  = 1725033/244252

3 + 244252/1725033  =

 

3.14159......=   "pi"

 

Actually....the first "3"  should have been the tipoff....LOL!!!!

 

P.S. - it's accurate to 12 decimal places

 

 

 

 

cool cool cool

CPhill  Apr 15, 2017
edited by CPhill  Apr 16, 2017
 #2
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BRAVO, CPhill !!!.

Guest Apr 15, 2017

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