计算:1/1×4+1/4×7+1/7×10+…+1/2005×2008.

问题描述:

计算:

1
1×4
+
1
4×7
+
1
7×10
+…+
1
2005×2008

1
1×4
+
1
4×7
+
1
7×10
+…+
1
2005×2008

=
1
3
(1-
1
4
)+
1
3
1
4
-
1
7
)+
1
3
1
7
-
1
10
)+…+
1
3
1
2005
-
1
2008

=
1
3
(1-
1
2008

=
669
2008