1/1×3+1/3×5+……+1/9×11=简便运算

题目

1/1×3+1/3×5+……+1/9×11=简便运算

答案

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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