2/1×3+2/3×5+2/5×7+…+2/2001×2003+2/2003×2005．

题目

2

1×3

+

2

3×5

+

2

5×7

+…+

2

2001×2003

+

2

2003×2005

答案

2

1×3

+

2

3×5

+

2

5×7

+…+

2

2001×2003

+

2

2003×2005

=1-

1

3

+

1

3

-

1

5

+

1

5

+…+

1

2001

-

1

2003

+

1

2003

-

1

2005

=1-

1

2005

=

2004

2005

．