数列{14n2-1}的前n项和为Sn,则limn→∞Sn=______.-数学

题目简介

数列{14n2-1}的前n项和为Sn,则limn→∞Sn=______.-数学

题目详情

数列{
1
4n2-1
}的前n项和为Sn,则
lim
n→∞
Sn=______.
题型:填空题难度:中档来源:江西

答案

an=class="stub"1
4n2-1
=class="stub"1
(2n-1)•(2n+1)
=class="stub"1
2
(class="stub"1
2n-1
-class="stub"1
2n+1
)

∴Sn=a1+a2+…+an
=class="stub"1
2
[(1-class="stub"1
3
)+(class="stub"1
3
-class="stub"1
5
)+…+(class="stub"1
2n-1
-class="stub"1
2n+1
)]

=class="stub"1
2
(1-class="stub"1
2n+1
)

lim
n→∞
Sn=
lim
n→∞
class="stub"1
2
(1-class="stub"1
2n+1
)=class="stub"1
2

故答案为:class="stub"1
2

更多内容推荐