问题 填空题
设Sn=
1
1×4
+
1
4×7
+…+
1
(3n-2)(3n+1)
则S10=______.
答案

∵Sn=

1
1×4
+
1
4×7
+…+
1
(3n-2)(3n+1)

=

1
3
(1-
1
4
+
1
4
-
1
7
+…+
1
3n-2
-
1
3n+1
)

=

1
3
(1-
1
3n+1
)

s10=

1
3
(1-
1
31
)=
10
31

故答案为:

10
31

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