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**+1 **

[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

CPhill
Apr 15, 2017