+0

# Continued Fraction......

0
130
2

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
Sort:

#1
+75352
+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
edited by CPhill  Apr 16, 2017
#2
0

BRAVO, CPhill !!!.

Guest Apr 15, 2017

### 4 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details