■x^1/2に収束する分数列(その12)

  a1=1,b1=1

  an+1=2an+3bn

  bn+1=an+2bn

を繰り返す.

[Q]このとき,an/bn→?

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[A]

 a1=1,b1=1,a1/b1=1

 a2=5,b2=3,a2/b2=1.6666666

 a3=19,b3=11,a3/b3=1.7272729

 a4=71,b4=41,a4/b4=1.7317073

 a5=265,b5=153,a5/b5=1.7320261

 a6=989,b6=571,a6/b6=1.732049

 an/bn→√3

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