Number patterns of fractions

Question

I can't seem to find a difference for this number pattern ..

Given a sequence ...

$1, 2/3 , 4/7 , 8/15 , 16/31 ... $

What is the next term of the sequence ?

I can't seem to spot a difference between them .. Anyone else can ? Thanks for the help !

Look at the numerators and denominators separately. Can you see the patterns? — Justin Benfield, Apr 13 '16 at 08:57

score 1 · Answer 1 · answered Apr 13 '16 at 08:20

1

For any given fraction in the sequence:

The numerator is the previous denominator +1.

The denominator is 2 times the previous denominator + 1.

answered Apr 13 '16 at 08:20

RuneOwl73

Of course, the first term can be written as $1/1$. – RuneOwl73 Apr 13 '16 at 08:23

score 0 · Answer 2 · answered Apr 13 '16 at 10:19

0

$$\left \{ \frac{2^{n-1}}{2^{n}-1} \right \}_{n=1}^{\infty}$$

answered Apr 13 '16 at 10:19

Ng Chung Tak

2 Answers2