已知函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211441797211/SYS201311031012114417972020_ST/0.png)
.
(Ⅰ)若函数在区间
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211441797211/SYS201311031012114417972020_ST/1.png)
(其中a>0)上存在极值,求实数a的取值范围;
(Ⅱ)如果当x≥1时,不等式
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211441797211/SYS201311031012114417972020_ST/2.png)
恒成立,求实数k的取值范围;
(Ⅲ)求证[(n+1)!]
2>(n+1)•e
n-2(n∈N
*).
考点分析:
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+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211441797211/SYS201311031012114417972019_ST/1.png)
=1(a>b>0)的离心率为
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=0相切.
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已知数列{a
n},{b
n}满足:a
1=3b
1=3,a
2=6,b
n+1=2b
n-2
n,b
n=a
n-na
n-1(n≥2,n∈N
*).
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211441797211/SYS201311031012114417972018_ST/0.png)
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n}的通项公式;
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n}的前n项和S
n.
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211441797211/SYS201311031012114417972017_ST/images0.png)
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211441797211/SYS201311031012114417972017_ST/0.png)
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求:
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211441797211/SYS201311031012114417972015_ST/4.png)
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