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已知数列{an}满足a1=5,a2=5,an+1=an+6an-1(n≥2,n∈N*).(...
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已知数列{a
n}满足a
1=5,a
2=5,a
n+1=a
n+6a
n-1(n≥2,n∈N
*).
(1)求证:当n≥2时,{a
n+2a
n-1}和{a
n-3a
n-1}均为等比数列;
(2)求证:当k为奇数时,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF4AAAAqCAYAAAA6Yey5AAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
;
(3)求证:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAqCAYAAAC5pdWCAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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=
)
(n∈N
*).
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOkAAAAjCAYAAABxRC0xAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
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(1)求a2,a3;
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,求数列{bn}的通项公式;
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.
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOkAAAAjCAYAAABxRC0xAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
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)
(1)求a2,a3;
(2)令
,求数列{bn}的通项公式;
(3)已知f(n)=6an+1-3an,求证:
.
-
已知数列{an}满足a1=5,a2=5,an+1=an+6an-1(n≥2,n∈N*),若数列{an+1+λan}是等比数列.
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)求证:当k为奇数时,
;
(Ⅲ)求证:
(n∈N*)
-
已知数列{an}满足a1=5,a2=5,an+1=an+6an-1(n≥2,n∈N*).
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(2)求证:当k为奇数时,
;
(3)求证:
(n∈N*).
-
已知数列{an}满足a1=5,a2=5,an+1=an+6an-1(n≥2,n∈N*).
(1)求证:当n≥2时,{an+2an-1}和{an-3an-1}均为等比数列;
(2)求证:当k为奇数时,
;
(3)求证:
(n∈N*).
-
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(1)求证:当n≥2时,{an+2an-1}和{an-3an-1}均为等比数列;
(2)求证:当k为奇数时,
;
(3)求证:
(n∈N*).
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(2)求数列{an}的通项公式;
(3)设3nbn=n(3n-an),且|b1|+|b2|++|bn|<m对于n∈N*恒成立,求m的取值范围.
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是等差数列;
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-
已知数列{an}满足a1=5,a2=5,an+1=an+6an-1(n≥2,n∈N*)
(1)求出所有使数列{an+1+λan}成等比数列的λ值,并说明理由.
(2)求数列{an}的通项公式.