1/(1×3)+1/(3×5)+1/(5×7)…+1/(99×101)=( )简便计算

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1/(1×3)+1/(3×5)+1/(5×7)…+1/(99×101)=( )简便计算
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1/(1×3)+1/(3×5)+1/(5×7)…+1/(99×101)=( )简便计算
1/(1×3)+1/(3×5)+1/(5×7)…+1/(99×101)=( )简便计算

1/(1×3)+1/(3×5)+1/(5×7)…+1/(99×101)=( )简便计算
1/(1×3)+1/(3×5)+1/(5×7)…+1/(99×101)
=1/2(1-1/3+1/3-1/5+1/5-1/7+…+1/99-1/101)
=1/2(1-1/101)
=50/101

100/101