脑壳短路老a1>0,a(n+1)=3(1+an)/3+an (递归数列),为什么0 < an < 3
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脑壳短路老
a1>0,a(n+1)=3(1+an)/3+an (递归数列),为什么0 < an < 3
a1>0,a(n+1)=3(1+an)/3+an (递归数列),为什么0 < an < 3
![脑壳短路老a1>0,a(n+1)=3(1+an)/3+an (递归数列),为什么0 < an < 3](/uploads/image/z/17686158-6-8.jpg?t=%E8%84%91%E5%A3%B3%E7%9F%AD%E8%B7%AF%E8%80%81a1%3E0%2Ca%28n%2B1%29%3D3%281%2Ban%29%2F3%2Ban+%28%E9%80%92%E5%BD%92%E6%95%B0%E5%88%97%29%2C%E4%B8%BA%E4%BB%80%E4%B9%880+%3C+an+%3C+3)
用数学归纳法算
A2=3-6/(3+A1)
∵A1>0
∴0<A2<3
再假设0<An<3
A(n+1)=3(1+an)/3+an =3-6/(3+An)
∴0<A(n+1)<3
得证
A2=3-6/(3+A1)
∵A1>0
∴0<A2<3
再假设0<An<3
A(n+1)=3(1+an)/3+an =3-6/(3+An)
∴0<A(n+1)<3
得证
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