1/1×3+1/3×5+……+1/9×11=简便运算
问题描述：
1/1×3+1/3×5+……+1/9×11=简便运算
答
1/n(n+2)=[1/n-1/(n+2)]/2
1/1×3+1/3×5+……+1/9×11=(1-1/3)/2+(1/3-1/5)/2+....+(1/9-1/11)/2=(1-1/3+1/3-1/5+....+1/9-1/11)/2=(1-1/11)/2=10/11x2=5/11
答
1/(1×3)+1/(3×5)+……+1/(9×11)
=1/2×(1-1/3)+1/2×(1/3-1/5)+……+1/2×(1/9-1/11)
=1/2×(1-1/3+1/3-1/5+……+1/9-1/11)
=1/2×(1-1/11)
=1/2×10/11
=5/11
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