求数列11×3,12×4,13×5,…,1n(n+2),…的前n项和S.-数学

题目简介

求数列11×3,12×4,13×5,…,1n(n+2),…的前n项和S.-数学

题目详情

求数列
1
1×3
1
2×4
1
3×5
,…,
1
n(n+2)
,…的前n项和S.
题型:解答题难度: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

∴Sn=class="stub"1
2
[(1-class="stub"1
3
)+(class="stub"1
2
-class="stub"1
4
)+…+(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"3
4
-class="stub"1
2n+2
-class="stub"1
2n+4

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