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已知2/1=1-2/1,6/1=2/1-3/1,12/1=3/1-4/1,...求2/1-6/1-12/1-20/1-30/1-42/1.
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已知2/1=1-2/1,6/1=2/1-3/1,12/1=3/1-4/1,...求2/1-6/1-12/1-20/1-30/1-42/1.
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答案和解析
1/2-1/6-1/12-1/20-1/30-1/42
=1/2-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)-(1/6-1/7)
=1/2-1/2+1/3-1/3+1/4--1/4+1/5-1/5+1/6-1/6+1/7
=1/7
=1/2-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)-(1/6-1/7)
=1/2-1/2+1/3-1/3+1/4--1/4+1/5-1/5+1/6-1/6+1/7
=1/7
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