定义:F(x,y)=yx(x>0,y>0),设数列{an}满足an=F(n,1)F(2,n),若Sn为数列{anan+1}的前n项和,则下列说法正确的是()A.Sn>lB.Sn≥lC.Sn<1D.Sn

题目简介

定义:F(x,y)=yx(x>0,y>0),设数列{an}满足an=F(n,1)F(2,n),若Sn为数列{anan+1}的前n项和,则下列说法正确的是()A.Sn>lB.Sn≥lC.Sn<1D.Sn

题目详情

定义:F(x,y)=yx(x>0,y>0),设数列{an}满足an=
F(n,1)
F(2,n)
,若Sn为数列{
anan+1
}的前n项和,则下列说法正确的是(  )
A.Sn>lB.Sn≥lC.Sn<1D.Sn≤l
题型:单选题难度:偏易来源:不详

答案

∵数列{an}满足an=
F(n,1)
F(2,n)
,∴an=
1n
n2
=class="stub"1
n2

anan+1
=
class="stub"1
n2
•class="stub"1
(n+1)2
=class="stub"1
n(n+1)
=class="stub"1
n
-class="stub"1
n+1

Sn=(1-class="stub"1
2
)+(class="stub"1
2
-class="stub"1
3
)+
…+(class="stub"1
n
-class="stub"1
n+1
)

=1-class="stub"1
n+1
<1.
即Sn<1.
故选C.

更多内容推荐