若Sn=11•2+12•3+13•4…+1n•(n+1)(n∈N*),则S10等于()A.89B.910C.1011D.1112-数学

题目简介

若Sn=11•2+12•3+13•4…+1n•(n+1)(n∈N*),则S10等于()A.89B.910C.1011D.1112-数学

题目详情

Sn=
1
1•2
+
1
2•3
+
1
3•4
…+
1
n•(n+1)
(n∈N*)
,则S10等于(  )
A.
8
9
B.
9
10
C.
10
11
D.
11
12
题型:单选题难度:中档来源:不详

答案

Sn=class="stub"1
1•2
+class="stub"1
2•3
+class="stub"1
3•4
+…+class="stub"1
n(n+1)

=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
=class="stub"n
n+1

S10=class="stub"10
11

故选C.

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