1/1X3+1/3X5+…….+1/99X101

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1/1X3+1/3X5+…….+1/99X101=1/2(1-1/3)+1/2(1/3-1/5)+…….+1/2(1/99-1/101)=1/2(1-1/3+1/3-1/5+……+1/99-1/101)=1/2(1-1/101)=1/2*100/101=50/101...

千问 | 2008-9-4 13:18:58 | 显示全部楼层

1-2/3+2/3-3/5+.......+50/99-51/101=1-51/101=50/101答案是50/101...

千问 | 2008-9-4 13:18:58 | 显示全部楼层

=1/2(1-1/3+1/3-1/5+1/5-……-1/99+1/99-1/101)=1/2(1-1/101)=50/101...

千问 | 2008-9-4 13:18:58 | 显示全部楼层

1/(1×3)+1/(3×5)+···+1/(99×101)=(1-(1/3))/2+((1/3)-(1/5))/2+···+((1/99)-(1/101))/2=(1-(1/3)+(1/3)-(1/5)+···+(1/99)-(1/101))/2=(1-(1/101))/2=50/101...

千问 | 2008-9-4 13:18:58 | 显示全部楼层

约分啊最后为101...

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