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已知函数,数列{an}满足a1=1,an+1=f(an),n∈N*,(Ⅰ)求证:数列是等差...
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已知函数
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEcAAAAjCAYAAADG1RdTAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
,数列{a
n}满足a
1=1,a
n+1=f(a
n),n∈N
*,
(Ⅰ)求证:数列
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAqCAYAAABLGYAnAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAGASURBVFhH7VeLsYQgDKQyeqIdmqEUSskjRJ9A
FHHxPe/mzhnnnDll89nNgqEHL/MgNr0pePRkjSUf8dphmQdHxph0PwGekw3kvuBg27Gef8v+eYTL
A4Z1LrcLGOMmCIcBll+9FnhwXEqX5td919GaVeb5JetpwisOI47eqqQKcJ7VNXlWQqG/dSTaCwrw
SN4asjMe2evUjgXrsqO6OaMI23DT0qbsc/7cx5fKlrkJeC7JvQw/CoRJvbZ2y/wfAmBgnfkSZhnV
WQsv/9/vedoYsc7/knBNawelJjMgbxgDyI++1DQbNzKuKpB3sOp0hwyTPo3ASos6IJQXem3SJ5Zq
BjNJKg5wMNdnwZFndC21lcZe9JdZX3wwDC4VuXf29zcTv8ciARVfvi+A19rJjPdw0X5WR/k8vgKe
eYwUU1usD0kByZQAb8DB+ZzKDpWA8/5DyfK8AhPgMrFckB1fK8tz6J0hM/LRgrYNIKDkvAaceZXp
KsmLjgiDD1eo8+Lngv8AJBIkFIQAP64AAAAASUVORK5CYII=
)
是等差数列;
(Ⅱ)令b
n=a
n-1•a
n(n≥2),b
1=3,S
n=b
1+b
2+…+b
n,若
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE8AAAAjCAYAAADVAlenAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
对一切n∈N
*成立,求最小正整数m.
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