1/1*3+1/3*5+1/5*7···+1/99*101

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1/1*3+1/3*5+1/5*7···+1/99*101
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1/1*3+1/3*5+1/5*7···+1/99*101
1/1*3+1/3*5+1/5*7···+1/99*101

1/1*3+1/3*5+1/5*7···+1/99*101
原式=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+.+1/2(1/99-1/101)
=1/2(1-1/3+1/3-1/5+1/5-1/7.-1/101)
=1/2(1-1/101)
=1/2*100/101
=50/101
这种题都有固定规律

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