我们知道1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,并依此计算1/1x3+1/3x5+1/5x7+.1/2003x2005

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我们知道1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,并依此计算1/1x3+1/3x5+1/5x7+.1/2003x2005

我们知道1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,并依此计算1/1x3+1/3x5+1/5x7+.1/2003x2005
我们知道1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,并依此计算1/1x3+1/3x5+1/5x7+.1/2003x2005

我们知道1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,并依此计算1/1x3+1/3x5+1/5x7+.1/2003x2005
1/1x3+1/3x5+1/5x7+.1/2003x2005
=(1/2)(1-1/3)+(1/2)(1/3-1/5)+………………+(1/2)(1/2003-1/2005)
=(1/2)*[1-1/3+1/3-1/5+…………+1/2003-1/2005]
=(1/2)*(1-1/2005)
=(1/2)*(2004/2005)
=1002/2005

原式=(1/2)[1/1-1/3]+(1/2)[1/3-1/5]+(1/2)[1/5-1/7]+…+(1/2)[1/2003-1/2005)]
=(1/2)[(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+…+(1/2003-1/2005)]
=(1/2)[1/1-1/2005]
=1002/2005