> 数学 >
求和:
1
1×4
+
1
4×7
+…+
1
(3n-2)×(3n+1)
= ___ .
人气:254 ℃ 时间:2020-02-04 09:39:17
解答
设Sn=
1
1×4
+
1
4×7
+…+
1
(3n-2)×(3n+1)

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

所以Sn=
n
(3n+1)

故答案为
n
(3n+1)
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