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Repeating Continued Fractions

​
number of sequence terms
4
initial term
1
a
1
b
1
c
1
d
1
e
1
f
1
g
1
h
1
i
1
j
1
Periodic Sequence:
{1,1,1,1}
Truncated Continued Fraction:
1+
1
1+
1
1+
1
1+
1
1+
1
1+
1
1+
1
1+
1
1+
1
1+
1
1
Exact Number:
1
2
(1+
5
)
Convergents:
2,
3
2
,
5
3
,
8
5
,
13
8
,
21
13
,
34
21
,
55
34
,
89
55
,
144
89
The continued fraction expansion of a quadratic irrational is eventually periodic; the converse is also true.
The repeating sequence, the initial part of the continued fraction form, the value, and the first few convergents to that value are shown.
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