数学天才请进来1/1*3+1/3*5+1/5*7+···+1/2003*2005=(1/2003-1)*(1/2002-1)*(1/2001-1)*···*(1/1001-1)*(1/1001-1)=
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![数学天才请进来1/1*3+1/3*5+1/5*7+···+1/2003*2005=(1/2003-1)*(1/2002-1)*(1/2001-1)*···*(1/1001-1)*(1/1001-1)=](/uploads/image/z/6822217-1-7.jpg?t=%E6%95%B0%E5%AD%A6%E5%A4%A9%E6%89%8D%E8%AF%B7%E8%BF%9B%E6%9D%A51%2F1%2A3%2B1%2F3%2A5%2B1%2F5%2A7%2B%C2%B7%C2%B7%C2%B7%2B1%2F2003%2A2005%3D%EF%BC%881%2F2003-1%EF%BC%89%2A%EF%BC%881%2F2002-1%EF%BC%89%2A%EF%BC%881%2F2001-1%EF%BC%89%2A%C2%B7%C2%B7%C2%B7%2A%EF%BC%881%2F1001-1%EF%BC%89%2A%EF%BC%881%2F1001-1%EF%BC%89%3D)
数学天才请进来1/1*3+1/3*5+1/5*7+···+1/2003*2005=(1/2003-1)*(1/2002-1)*(1/2001-1)*···*(1/1001-1)*(1/1001-1)=
数学天才请进来
1/1*3+1/3*5+1/5*7+···+1/2003*2005=
(1/2003-1)*(1/2002-1)*(1/2001-1)*···*(1/1001-1)*(1/1001-1)=
数学天才请进来1/1*3+1/3*5+1/5*7+···+1/2003*2005=(1/2003-1)*(1/2002-1)*(1/2001-1)*···*(1/1001-1)*(1/1001-1)=
1.原式=(1/1-1/3+1/3-1/5+1/5-1/7+……+1/2003-1/2005)×1/2
=(1-1/2005)×1/2
=2004/2005×1/2
=1002/2005
2.
1/2003-1=-2002/2003
1/2002-1=-2001/2002
1/2001-1=-2000/2001
...
1/1001-1=-1000/1001
1/1000-1=-999/1000
因为共有2003-1000+1=1004个负数相乘,所以结果为正
得:
2002/2003×2001/2002×2000/2001×……×1000/1001×999/1000
=999/2003
1/1*3+1/3*5+1/5*7+···+1/2003*2005=0.5(1-1/3+1/3-1/5+……+1/2003-1/2005)=0.5(1-1/2005)
1/2003-1)*(1/2002-1)*(1/2001-1)*···*(1/1001-1)*(1/1001-1
最后一个是1/1001-1??