(理)数列11×3,12×4,13×5,14×6,…1n(n+2)的前8项和为()A.2945B.920C.5845D.910-数学

题目简介

(理)数列11×3,12×4,13×5,14×6,…1n(n+2)的前8项和为()A.2945B.920C.5845D.910-数学

题目详情

(理)数列
1
1×3
1
2×4
1
3×5
1
4×6
,…
1
n(n+2)
的前8项和为(  )
A.
29
45
B.
9
20
C.
58
45
D.
9
10
题型:单选题难度:偏易来源:不详

答案

因为数列的通项class="stub"1
n(n+2)
=class="stub"1
2
(class="stub"1
n
-class="stub"1
n+2
)

所以数列{class="stub"1
n(n+2)
}的前8项的和为:
S8=class="stub"1
1×3
+class="stub"1
2×4
+class="stub"1
3×5
+…+class="stub"1
7×9
+class="stub"1
8×10

=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
7
-class="stub"1
9
)+(class="stub"1
8
-class="stub"1
10
)]

=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
7
-class="stub"1
9
+class="stub"1
8
-class="stub"1
10
]

=class="stub"1
2
[1+class="stub"1
2
-class="stub"1
9
-class="stub"1
10
]

=class="stub"29
45

故选A.

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