问题 填空题
计算:
2000-1990+1980-1970+…+20-10
(1-
1
2
)(1-
1
3
)(1-
1
4
)(1-
1
5
)…(1-
1
999
)(1-
1
1000
)
=______.
答案

2000-1990+1980-1970+…+20+10
(1-
1
2
)(1-
1
3
)(1-
1
4
)(1-
1
5
)..(1-
1
999
)(1-
1
1000
)

=

(2000-1990)+(1980-1970)+…+(20-10)
1
2
2
3
3
4
4
5
..
998
999
999
1000

=(

100个10
10+10+10+…+10
1
1000
=
1000
1
1000
=1000000.

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