2/(1*2*3)+2/(2*3*4)+2/(3*4*5).2/(8*9*10)一乘以二乘以三分之二加上二乘以三乘以四分之二、、、、、、八乘以九乘以十分之二,好难,直接计算通分太难,应该有简便算法~
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 06:22:06
![2/(1*2*3)+2/(2*3*4)+2/(3*4*5).2/(8*9*10)一乘以二乘以三分之二加上二乘以三乘以四分之二、、、、、、八乘以九乘以十分之二,好难,直接计算通分太难,应该有简便算法~](/uploads/image/z/6992542-46-2.jpg?t=2%2F%EF%BC%881%2A2%2A3%EF%BC%89%2B2%2F%EF%BC%882%2A3%2A4%EF%BC%89%2B2%2F%EF%BC%883%2A4%2A5%EF%BC%89.2%2F%EF%BC%888%2A9%2A10%EF%BC%89%E4%B8%80%E4%B9%98%E4%BB%A5%E4%BA%8C%E4%B9%98%E4%BB%A5%E4%B8%89%E5%88%86%E4%B9%8B%E4%BA%8C%E5%8A%A0%E4%B8%8A%E4%BA%8C%E4%B9%98%E4%BB%A5%E4%B8%89%E4%B9%98%E4%BB%A5%E5%9B%9B%E5%88%86%E4%B9%8B%E4%BA%8C%E3%80%81%E3%80%81%E3%80%81%E3%80%81%E3%80%81%E3%80%81%E5%85%AB%E4%B9%98%E4%BB%A5%E4%B9%9D%E4%B9%98%E4%BB%A5%E5%8D%81%E5%88%86%E4%B9%8B%E4%BA%8C%EF%BC%8C%E5%A5%BD%E9%9A%BE%EF%BC%8C%E7%9B%B4%E6%8E%A5%E8%AE%A1%E7%AE%97%E9%80%9A%E5%88%86%E5%A4%AA%E9%9A%BE%EF%BC%8C%E5%BA%94%E8%AF%A5%E6%9C%89%E7%AE%80%E4%BE%BF%E7%AE%97%E6%B3%95%EF%BD%9E)
2/(1*2*3)+2/(2*3*4)+2/(3*4*5).2/(8*9*10)一乘以二乘以三分之二加上二乘以三乘以四分之二、、、、、、八乘以九乘以十分之二,好难,直接计算通分太难,应该有简便算法~
2/(1*2*3)+2/(2*3*4)+2/(3*4*5).2/(8*9*10)
一乘以二乘以三分之二加上二乘以三乘以四分之二、、、、、、八乘以九乘以十分之二,好难,直接计算通分太难,应该有简便算法~
2/(1*2*3)+2/(2*3*4)+2/(3*4*5).2/(8*9*10)一乘以二乘以三分之二加上二乘以三乘以四分之二、、、、、、八乘以九乘以十分之二,好难,直接计算通分太难,应该有简便算法~
简便算法是这样的:
2/(1*2*3)=1/1-2*(1/2)+1/3
2/(2*3*4)=1/2-2*(1/3)+1/4
...
2/(8*9*10)=1/8-2*(1/9)+1/10
叠加相消得:
原式=1/1-1/2-1/9+1/10=22/45
答案不知道有没有错,不过方法是这样的...
希望我的回答让你满意
2/(1*2*3)=(1/2)*2*[1/(1*2)+1/(2*3)]=1/3
以次类推,答案为22/45
我不只到
1/1*2*3=(1/1*2-1/2*3)÷2
1/2*3*4=(1/2*3-1/3*4)÷2
1/3*4*5=(1/3*4-1/4*5)÷2
......
1/8*9*1=(1/8*9-1/9*10)÷2
2/(1*2*3)+2/(2*3*4)+2/(3*4*5)。。。。。2/(8*9*10)
=(2*1/2)(1/1*2*3+1/2*3...
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1/1*2*3=(1/1*2-1/2*3)÷2
1/2*3*4=(1/2*3-1/3*4)÷2
1/3*4*5=(1/3*4-1/4*5)÷2
......
1/8*9*1=(1/8*9-1/9*10)÷2
2/(1*2*3)+2/(2*3*4)+2/(3*4*5)。。。。。2/(8*9*10)
=(2*1/2)(1/1*2*3+1/2*3*4+1/3*4*5+........1/8*9*10
=(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+......+1/7*8-1/8*9+1/8*9-1/9*10)
=(1/1*2-1/9*10)
=(1/2-1/90)
=44/90
=22/45
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