limn→∞[11•4+14•7+17•10+…+1(3n-2)(3n+1)]=______.-数学

题目简介

limn→∞[11•4+14•7+17•10+…+1(3n-2)(3n+1)]=______.-数学

题目详情

lim
n→∞
[
1
1•4
+
1
4•7
+
1
7•10
+…+
1
(3n-2)(3n+1)
]
=______.
题型:填空题难度:中档来源:云南

答案

lim
n→∞
[class="stub"1
1•4
+class="stub"1
4•7
+class="stub"1
7•10
+…+class="stub"1
(3n-2)(3n+1)
]

=
lim
n→∞
class="stub"1
3
[(1-class="stub"1
4
)+(class="stub"1
4
-class="stub"1
7
)+…+(class="stub"1
3n-2
-class="stub"1
3n+1
)

=
lim
n→∞
class="stub"1
3
(1-class="stub"1
3n+1
)

=
lim
n→∞
class="stub"1
3
•class="stub"3n
3n+1
=class="stub"1
3

故答案为class="stub"1
3

更多内容推荐