首页
已知函数f(x)=x2-x+1,数列{an}满足:a1=2,an+1=f(an),其中n∈...
试题详情
已知函数f(x)=x
2-x+1,数列{a
n}满足:a
1=2,a
n+1=f(a
n),其中n∈N
*.
(Ⅰ)证明:1<a
n<a
n+1;
(Ⅱ)证明:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAqCAYAAAC5pdWCAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
.
相关试题
-
已知函数f(x)=x2-x+1,数列{an}满足:a1=2,an+1=f(an),其中n∈N*.
(Ⅰ)证明:1<an<an+1;
(Ⅱ)证明:
.
-
已知函数f(x)=x2-x+1,数列{an}满足:a1=2,an+1=f(an),其中n∈N*.
(Ⅰ)证明:1<an<an+1;
(Ⅱ)证明:
.
-
已知函数f(x)=
x2-x+2,数列{an}满足递推关系式:an+1=f(an),n≥1,n∈N,且a1=1.
(1)求a2,a3,a4的值;
(2)用数学归纳法证明:当n≥5时,an<2-
;
(3)证明:当n≥5时,有
.
-
已知函数f(x)=
(x≠-1).设数列{an}满足a1=1,an+1=f(an),数列{bn}满足bn=|an-
|,Sn=b1+b2+…+bn(n∈N*).
(Ⅰ)用数学归纳法证明bn≤
;
(Ⅱ)证明Sn<
.
-
已知函数
,数列{an}满足a1=1,an+1=f(an);数列{bn}满足
,
,其中Sn为数列{bn}前n项和,n=1,2,3…
(1)求数列{an}和数列{bn}的通项公式;
(2)设
,证明Tn<5.
-
已知函数
,数列{an}满足an+1=f'n(an),a1=3.
(1)求a2,a3,a4;
(2)根据猜想数列{an}的通项公式,并证明;
(3)求证:
.
-
已知函数
,无穷数列{an}满足an+1=f(an)(n∈N*).
(1)求a1的值使得{an}为常数列;
(2)若a1>2,证明:an>an+1;
(3)若a1=3,求证:
.
-
已知函数
,数列{an}满足a1=a(a≠-2,a∈R),an+1=f(an)(n∈N*).
(1)若数列{an}是常数列,求a的值;
(2)当a1=2时,记
,证明数列{bn}是等比数列,并求出通项公式an.
-
已知函数
,数列{an}满足a1=a(a≠-2,a∈R),an+1=f(an)(n∈N*).
(1)若数列{an}是常数列,求a的值;
(2)当a1=2时,记
,证明数列{bn}是等比数列,并求出通项公式an.
-
已知函数
,数列{an}满足a1=a(a≠-2,a∈R),an+1=f(an)(n∈N*).
(1)若数列{an}是常数列,求a的值;
(2)当a1=2时,记
,证明数列{bn}是等比数列,并求出通项公式an.