求一道数学简便计算题!太急了!100分那!(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)1/2是二分之一
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![求一道数学简便计算题!太急了!100分那!(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)1/2是二分之一](/uploads/image/z/4328624-56-4.jpg?t=%E6%B1%82%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%E9%A2%98%21%E5%A4%AA%E6%80%A5%E4%BA%86%21100%E5%88%86%E9%82%A3%21%EF%BC%881%2B1%2F2%2B1%2F3%2B1%2F4%EF%BC%89%2A%EF%BC%881%2F2%2B1%2F3%2B1%2F4%2B1%2F6%EF%BC%89-%EF%BC%881%2B1%2F2%2B1%2F3%2B1%2F4%2B1%2F5%EF%BC%89%2A%EF%BC%881%2F2%2B1%2F3%2B1%2F4%EF%BC%891%2F2%E6%98%AF%E4%BA%8C%E5%88%86%E4%B9%8B%E4%B8%80)
求一道数学简便计算题!太急了!100分那!(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)1/2是二分之一
求一道数学简便计算题!太急了!100分那!
(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)
1/2是二分之一
求一道数学简便计算题!太急了!100分那!(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)1/2是二分之一
(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)
=(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4)*(1/2+1/3+1/4)-(1/5)*(1/2+1/3+1/4)
=(1+1/2+1/3+1/4)*(1/6)-(1/5)*(1/2+1/3+1/4)
=1/6+(1/2+1/3+1/4)*(1/6)-(1/5)*(1/2+1/3+1/4)
=1/6+(1/2+1/3+1/4)*(-1/30)
=47/360
没问题阿?
没问题啊!
设 (1/2+1/3+1/4)=m
原式=(1+m)(m+1/6)-(1+m+1/5)*m=m+1/6+m*m+m/6-(m+m*m+m/5)=m+1/6+m*m+m/6-m-m*m-m/5=1/6+m/6-m/5,因为m=13/12所以,原式=47/360
设a=1/2+1/3+1/4=13/12
原式
=(1+a)(a+1/6)-(1+a+1/5)a
=7a/6+1/6+a^2-a^2-6a/5
=1/6-a/30
=1/6-13/360
=47/360
原式=(1+1/2+1/3+1/4)*(1/2+1/3+1/4)+(1+1/2+1/3+1/4)*(1/6)-(1+1/2+1/3+1/4)*(1/2+1/3+1/4)-(1/5)*(1/2+1/3+1/4)
=(1+1/2+1/3+1/4)*(1/6)-(1/5)*(1/2+1/3+1/4)
=25/72-13/60
=125/360-78/360
=47/360
设 (1/2+1/3+1/4)=m
变成(1+m)(m+1/6)-(1+m+1/5)*m
然后先算了这个再带入m