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All rational numbers in (Posted on 2016-08-26) Difficulty: 3 of 5
The infinite sequence is defined as follows:
a1=1
for n ≥ 1, a2n= an+1
a2n+1=1/ a2n

Prove that every positive rational number occurs in the sequence exactly once.

No Solution Yet Submitted by Ady TZIDON    
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re: From N/D to n | Comment 4 of 10 |
(In reply to From N/D to n by Jer)

9/7 + 1 = 16/7, not 13/7


Is this not what you meant?:

7/13  135
13/7  134
6/7    67
7/6    66
1/6    33
6      32
5      16
4       8
3       4
2       2
1       

so that a135 = 7/13

Edited on August 28, 2016, 10:36 pm
  Posted by Charlie on 2016-08-28 22:27:57

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