求和:11×4+14×7+…+1(3n-2)×(3n+1)=______.-数学

题目简介

求和:11×4+14×7+…+1(3n-2)×(3n+1)=______.-数学

题目详情

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

答案

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

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

所以Sn=class="stub"n
(3n+1)

故答案为class="stub"n
(3n+1)

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