1\(2×3)+1\(3×4)+1\(4×5)+…+1\(1000×1001)=?
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![1\(2×3)+1\(3×4)+1\(4×5)+…+1\(1000×1001)=?](/uploads/image/z/1264335-15-5.jpg?t=1%5C%282%C3%973%29%2B1%5C%283%C3%974%29%2B1%5C%284%C3%975%29%2B%E2%80%A6%2B1%5C%281000%C3%971001%29%3D%3F)
1\(2×3)+1\(3×4)+1\(4×5)+…+1\(1000×1001)=?
1\(2×3)+1\(3×4)+1\(4×5)+…+1\(1000×1001)=?
1\(2×3)+1\(3×4)+1\(4×5)+…+1\(1000×1001)=?
1\(a*b)=1\a-1\b
故上式1\(2×3)+1\(3×4)+1\(4×5)+…+1\(1000×1001)
=1\2-1\3+1\3-1\4+1\4+1\5-……+1\1000-1\1001
=1\2-1\1001
=999/2002