11×3+12×4+13×5+14×6+…+1n(n+2)=()A.1n(n+2)B.12(1-1n+2)C.12(32-1n+1-1n+2)D.12(1-1n+1)-高二数学

题目简介

11×3+12×4+13×5+14×6+…+1n(n+2)=()A.1n(n+2)B.12(1-1n+2)C.12(32-1n+1-1n+2)D.12(1-1n+1)-高二数学

题目详情

1
1×3
+
1
2×4
+
1
3×5
+
1
4×6
+…+
1
n(n+2)
=(  )
A.
1
n(n+2)
B.
1
2
(1-
1
n+2
C.
1
2
3
2
-
1
n+1
-
1
n+2
D.
1
2
(1-
1
n+1
题型:单选题难度:中档来源:不详

答案

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

class="stub"1
1×3
+class="stub"1
2×4
+class="stub"1
3×5
+class="stub"1
4×6
+…+class="stub"1
n(n+2)

=class="stub"1
2
[(1-class="stub"1
3
)+(class="stub"1
2
-class="stub"1
4
)+(class="stub"1
3
-class="stub"1
5
)+(class="stub"1
4
-class="stub"1
6
)+…+(class="stub"1
n-2
-class="stub"1
n
)+(class="stub"1
n-1
-class="stub"1
n+1
)+(class="stub"1
n
-class="stub"1
n+2
)]
=class="stub"1
2
(1+class="stub"1
2
-class="stub"1
n+1
-class="stub"1
n+2

=class="stub"1
2
class="stub"3
2
-class="stub"1
n+1
-class="stub"1
n+2
),
故答案选C.

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