作业帮(1/1×2)＋(1/2×3)+(1/3×4)+(1/4×5)+.+(1/2004×2005)(1/1×3)+(1/3×5)+(1/5×7)+(1/7×9)+.+(1/19×21)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/09 04:34:41
(1/1×2)＋(1/2×3)+(1/3×4)+(1/4×5)+.+(1/2004×2005)(1/1×3)+(1/3×5)+(1/5×7)+(1/7×9)+.+(1/19×21)
(1/1×2)＋(1/2×3)+(1/3×4)+(1/4×5)+.+(1/2004×2005)
(1/1×3)+(1/3×5)+(1/5×7)+(1/7×9)+.+(1/19×21)
(1/1×2)＋(1/2×3)+(1/3×4)+(1/4×5)+.+(1/2004×2005)(1/1×3)+(1/3×5)+(1/5×7)+(1/7×9)+.+(1/19×21)
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题目：1）1/1*2+1/2*3+……+1/2004*2005
2）1/1*3+1/3*5+……1/19*21
1）原式=1-1/2+1/2-1/3+……+1/2004-1/2005=1-1/2005=2004/2005
2）原式=1/2*（1-1/3+1/3-1/5+……+1/19-1/21）=1/2*（1-1/21）=1/2*20/21=10/21
第一个为2004/2005
第二个为20/42
(1/1×2)＋(1/2×3)+(1/3×4)+(1/4×5)+......+(1/2004×2005)
=1-1/2+1/2-1/3+.......+1/2004-1/2005
=1-1/2005
=2004/2005
(1/1×3)+(1/3×5)+(1/5×7)+(1/7×9)+....+(1/19×21)
=1/2[1-1/3]+1/2[1/3-1/5]+....+1/2[1/19-1/21]
=1/2[1-1/3+1/3-1/5+.....+1/19-1/21]
=1/2[1-1/21]
=1/2*20/21
=10/21
(1/1×2)＋(1/2×3)+(1/3×4)+(1/4×5)+......+(1/2004×2005)
=（1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/2004-1/2005)
=1-1/2005
=2004/2005
(1/1×3)+(1/3×5)+(1/5×7)+(1/7×9)+....+(1/19×21)
=(1/2)...
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(1/1×2)＋(1/2×3)+(1/3×4)+(1/4×5)+......+(1/2004×2005)
=（1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/2004-1/2005)
=1-1/2005
=2004/2005
(1/1×3)+(1/3×5)+(1/5×7)+(1/7×9)+....+(1/19×21)
=(1/2)×(1-1/3)+(1/2)×(1/3-1/5)+(1/2)×(1/5-1/7)+……+(1/2)×(1/19-1/21)
=(1/2)×(1-1/3+1/3-1/5+1/5-1/7+……+1/19-1/21)
=(1/2)×(1-1/21)
=10/21
收起
1-1/2+1/2-1/3+1/3-1/4+.....+1/2004-1/2005
=1-1/2005=2004/2005
1/2(1-1/3+1/3-1/5+1/5-1/7+.....+1/19-1/21)
=1/2(1-1/21)
=1/2*20/21
=10/21