Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

The continued fraction that we looked at was this;

1
2+
2

1
2+

1
2+
2

1
1
2 +

2+
1
2+
1
2+
2

1
1
2 +

2+
1
2+
1
2+
1
2+
2

1
1
2 +

2+
1
2+
1
2+
1
2+
1
2+
2


To make the next continued fraction we replace the denominator of the last fraction with the
⎛ 1⎞
starting term ⎜ 2 + ⎟
⎝ 2⎠

1
Notice that the “next” continued fraction will be just 2 +

the last continued fraction

1
5
So the first fraction is 2 or
2
2

1
2
5
5
The second is 2 + (2 plus the reciprocal of )
...

5
5

12
12
5
1
The third continued fraction is 2 +
(2 plus the reciprocal of )
...

12
12

1
2

2

2

The series of fractions will be 2

2
5

5

12

2

5

...







2
5





2





5 × 2 + 2

So the next fraction will be

2+


So we get 2

1
2

2

2
5

2

5
12

2

12
12
=2
12 × 2 + 5
29

12
29

2

29
70

2

70
169

2

169

...



We can represent continued fractions in a code to save writing them out in full
...

It’s code is [2;2,2,2,2,2,2]
The denominator does not always have to be the same

---