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(1/11+1/12+1/13+1/14+1/15)×(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/13+1/14+1/15

分类: 作业答案 • 2022-07-08 12:59:57
问题描述：

(1/11+1/12+1/13+1/14+1/15)×(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/13+1/14+1/15

答

(1+1/11+1/12+1/13+1/14+1/15)×(1/11+1/12+1/13+1/14+1/15+1/16)-(1+1/11+1/12+1/13+1/14+1/15+1/16）×(1/11+1/12+1/13+1/14+1/15)
=(1/11+1/12+1/13+1/14+1/15)×(1/11+1/12+1/13+1/14+1/15+1/16)+(1/11+1/12+1/13+1/14+1/15+1/16）-(1/11+1/12+1/13+1/14+1/15)×(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/13+1/14+1/15）
=(1/11+1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/13+1/14+1/15）
=1/16

答

令a=1/12+1/13+1/14+1/15
原式=(1/11+a)(a+1/16)-(1/11+a+1/16)a
=(1/11+a)a+1/16(1/11+a)-(1/11+a)a-1/16a
=1/16(1/11+a)-1/16a
=1/176+1/16a-1/16a
=1/176

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