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1/1x3+1/3x5+1/5x7+...1/2001x2003中用了什么法则,将和式中的各分数转化为两个数之得
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1/1x3+1/3x5+1/5x7+...1/2001x2003中用了什么法则,将和式中的各分数转化为两个数之得
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答案和解析
1/1x3+1/3x5+1/5x7+...1/2001x2003
=(1/1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+...+(1/2001-1/2003)/2
=(1/1-1/3+1/3-1/5+1/5-1/7+...+1/2001-1/2003)/2
=(1-1/2003)/2
=2002/2003除以2
=1001/2003
=(1/1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+...+(1/2001-1/2003)/2
=(1/1-1/3+1/3-1/5+1/5-1/7+...+1/2001-1/2003)/2
=(1-1/2003)/2
=2002/2003除以2
=1001/2003
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