设Sn=11×4+14×7+…+1(3n-2)(3n+1)则S10=______.-数学

题目简介

设Sn=11×4+14×7+…+1(3n-2)(3n+1)则S10=______.-数学

题目详情

设Sn=
1
1×4
+
1
4×7
+…+
1
(3n-2)(3n+1)
则S10=______.
题型:填空题难度:中档来源:不详

答案

∵Sn=class="stub"1
1×4
+class="stub"1
4×7
+…+class="stub"1
(3n-2)(3n+1)

=class="stub"1
3
(1-class="stub"1
4
+class="stub"1
4
-class="stub"1
7
+…+class="stub"1
3n-2
-class="stub"1
3n+1
)

=class="stub"1
3
(1-class="stub"1
3n+1
)

s10=class="stub"1
3
(1-class="stub"1
31
)
=class="stub"10
31

故答案为:class="stub"10
31

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