bn13

由an+

3
bn=(an?1+
3
bn?1)2=
a2n?1
+3
b2n?1
+2an?1bn?1
3

以及an,bn均为正整数可知:

an=

a2n?1
+3
b2n?1
,bn=2an?1bn?1.

于是

an
bn
a2n?1
+3
b2n?1
2an?1bn?1
(
an?1
bn?1
)2+3
2
an?1
bn?1

令cn=

an
bn
,则cn=
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