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1X1/2X1/3+1/2X1/3X1/4+1/3X1/4X1/5+.+1/20X1/21X1/22等于几?
题目详情
1X1/2X1/3+1/2X1/3X1/4+1/3X1/4X1/5+.+1/20X1/21X1/22等于几?
▼优质解答
答案和解析
=1/2×(1/1×2-1/2×3)+1/2×(1/2×3-1/3×4)+……+1/2×(1/20×21-1/21×22)
=1/2×(1/1×2-1/2×3+1/2×3-1/3×4+……+1/20×21-1/21×22)
=1/2×(1/1×2-1/21×22)
=115/462
=1/2×(1/1×2-1/2×3+1/2×3-1/3×4+……+1/20×21-1/21×22)
=1/2×(1/1×2-1/21×22)
=115/462
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