问题 解答题
1
2
1+
1
2
+
1
3
(1+
1
2
)(1+
1
3
)
+
1
4
(1+
1
2
)(1+
1
3
)(1+
1
4
)
+…+
1
1999
(1+
1
2
)(1+
1
3
)…(1+
1
1999
)
答案

原式=

1
2
×4
(1+
1
2
)×4
+
1
3
×6
3
2
×
4
3
×6
+…+
1
1999
×1999×2
3
2
×
4
3
×…×
2000
1999
×1999×2

=

2
2×3
+
2
3×4
+…+
2
1999×2000

=(

1
2
-
1
3
+
1
3
-
1
4
+…+
1
1999
-
1
2000
)×2,

=(

1
2
-
1
2000
)×2,

=1-

1
1000

=

999
1000

单项选择题
单项选择题 A2型题