求(1/2003-1)x(1/2002-1)x(1/2001-1)x(1/2000-1)x(1/1999-1)...(1/1001-1)x(1/1000-1)的积(1/2003-1)(1/2002-1)(1/2001-1)(1/2000-1)(1/1999-1)...(1/1001-1) (1/1000-1)=(-2002/2003)(-2001/2002)(-2000/2001)(-1999/2000)…(-999/1000)1/2003-1=1/2003-2003/2
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![求(1/2003-1)x(1/2002-1)x(1/2001-1)x(1/2000-1)x(1/1999-1)...(1/1001-1)x(1/1000-1)的积(1/2003-1)(1/2002-1)(1/2001-1)(1/2000-1)(1/1999-1)...(1/1001-1) (1/1000-1)=(-2002/2003)(-2001/2002)(-2000/2001)(-1999/2000)…(-999/1000)1/2003-1=1/2003-2003/2](/uploads/image/z/142726-22-6.jpg?t=%E6%B1%82%EF%BC%881%2F2003-1%29x%281%2F2002-1%29x%281%2F2001-1%29x%281%2F2000-1%29x%281%2F1999-1%29...%281%2F1001-1%29x%281%2F1000-1%29%E7%9A%84%E7%A7%AF%EF%BC%881%2F2003-1%29%281%2F2002-1%29%281%2F2001-1%29%281%2F2000-1%29%281%2F1999-1%29...%281%2F1001-1%29+%281%2F1000-1%29%3D%28-2002%2F2003%29%28-2001%2F2002%29%28-2000%2F2001%29%28-1999%2F2000%29%E2%80%A6%28-999%2F1000%291%2F2003-1%3D1%2F2003-2003%2F2)
求(1/2003-1)x(1/2002-1)x(1/2001-1)x(1/2000-1)x(1/1999-1)...(1/1001-1)x(1/1000-1)的积(1/2003-1)(1/2002-1)(1/2001-1)(1/2000-1)(1/1999-1)...(1/1001-1) (1/1000-1)=(-2002/2003)(-2001/2002)(-2000/2001)(-1999/2000)…(-999/1000)1/2003-1=1/2003-2003/2
求(1/2003-1)x(1/2002-1)x(1/2001-1)x(1/2000-1)x(1/1999-1)...(1/1001-1)x(1/1000-1)的积
(1/2003-1)(1/2002-1)(1/2001-1)(1/2000-1)(1/1999-1)...(1/1001-1) (1/1000-1)
=(-2002/2003)(-2001/2002)(-2000/2001)(-1999/2000)…(-999/1000)
1/2003-1=1/2003-2003/2003=-2002/2003
1/2002-1=1/2002-2002/2002=-2001/2002
1/2001-1=1/2001-2001/2001=-2000/2001
这里我看懂了但是
=(-2002/2003)(-2001/2002)(-2000/2001)(-1999/2000)…(-999/1000)
=999/2003 是怎么运算出来的呀?
2004是怎么得到的啊?我我是小学毕业的看不懂,我儿子也弄不明白,这是初一的题,
求(1/2003-1)x(1/2002-1)x(1/2001-1)x(1/2000-1)x(1/1999-1)...(1/1001-1)x(1/1000-1)的积(1/2003-1)(1/2002-1)(1/2001-1)(1/2000-1)(1/1999-1)...(1/1001-1) (1/1000-1)=(-2002/2003)(-2001/2002)(-2000/2001)(-1999/2000)…(-999/1000)1/2003-1=1/2003-2003/2
首先可以确定总项数为 2004项
则 (1/2003-1)(1/2002-1)(1/2001-1)(1/2000-1)(1/1999-1)...(1/1001-1) (1/1000-1)
=(-2002/2003)(-2001/2002)(-2000/2001)(-1999/2000)…(-999/1000)
=999/2003
1/2003-1=1/2003-2003/2003=-2002/2003
1/2002-1=1/2002-2002/2002=-2001/2002
1/2001-1=1/2001-2001/2001=-2000/2001
……