limn→∞(1n+1-2n+1+3n+1-…+2n-1n+1-2nn+1)的值为()A.-1B.0C.12D.1-数学

题目简介

limn→∞(1n+1-2n+1+3n+1-…+2n-1n+1-2nn+1)的值为()A.-1B.0C.12D.1-数学

题目详情

lim
n→∞
(
1
n+1
-
2
n+1
+
3
n+1
-…+
2n-1
n+1
-
2n
n+1
)
的值为(  )
A.-1B.0C.
1
2
D.1
题型:单选题难度:中档来源:广东

答案

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

=
lim
n→∞
[1+3+5+…+(2n-1)]-[2+4+6+…+2n]
n+1

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

=
lim
n→∞
class="stub"-n
n+1

=-1.
故选A.

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