(1/2+1/4+1/6+1/8)-(1/3+1/6+1/9+1/12)+(1/4+1/8+1/12+1/16)-(1/5+1/10+1/15+1/20)

来源:学生作业帮助网 编辑:作业帮 时间:2024/12/04 01:59:13
(1/2+1/4+1/6+1/8)-(1/3+1/6+1/9+1/12)+(1/4+1/8+1/12+1/16)-(1/5+1/10+1/15+1/20)
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(1/2+1/4+1/6+1/8)-(1/3+1/6+1/9+1/12)+(1/4+1/8+1/12+1/16)-(1/5+1/10+1/15+1/20)
(1/2+1/4+1/6+1/8)-(1/3+1/6+1/9+1/12)+(1/4+1/8+1/12+1/16)-(1/5+1/10+1/15+1/20)

(1/2+1/4+1/6+1/8)-(1/3+1/6+1/9+1/12)+(1/4+1/8+1/12+1/16)-(1/5+1/10+1/15+1/20)
原式=(1/2)(1+1/2+1/3+1/4)-(1/3)(1+1/2+1/3+1/4)+(1/4)(1+1/2+1/3+1/4)-(1/5)(1+1/2+1/3+1/4)
=(1/2-1/3+1/4-1/5)(1+1/2+1/3+1/4)
=(13/60)*(25/12)=65/144

原式=1/2(1+1/2+1/3+1/4)-1/3(1+1/2+1/3+1/4)+1/4(1+1/2+1/3+1/4)-1/5(1+1/2+1/3+1/4)
=(1+1/2+1/3+1/4)(1/2-1/3+1/4-1/5)
=25/12*13/60
=65/144