观察下列算式,你发现了什么规律?你能根据发现的规律进行计算吗？
1/1*2=1-1/21/2*3=1/2-1/31/3*4=1/3-1/41/1*2+1/2*3+1/3*4+//4*51/2+1/6+1/12+1/20+1/30+1/...
1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
1/1*2+1/2*3+1/3*4+//4*5
1/2+1/6+1/12+1/20+1/30+1/42 展开
1/2*3=1/2-1/3
1/3*4=1/3-1/4
1/1*2+1/2*3+1/3*4+//4*5
1/2+1/6+1/12+1/20+1/30+1/42 展开
2个回答
展开全部
1/n(n+1)=1/n-1/n+1
1/1*2+1/2*3+1/3*4+//4*5
=1-1/2+1/2-1/3+1/3-1/4+1/5
=1-1/5
=4/5
1/2+1/6+1/12+1/20+1/30+1/42
=1/2+1/6+1/2*6+1/4*5+1/5*6+1/6*7
=1/2+1/6+1/2-1/6+1/4-1/5+1/5-1/6+1/6-1/7
=1/2+1/2+1/4-1/7
=31/28
1/1*2+1/2*3+1/3*4+//4*5
=1-1/2+1/2-1/3+1/3-1/4+1/5
=1-1/5
=4/5
1/2+1/6+1/12+1/20+1/30+1/42
=1/2+1/6+1/2*6+1/4*5+1/5*6+1/6*7
=1/2+1/6+1/2-1/6+1/4-1/5+1/5-1/6+1/6-1/7
=1/2+1/2+1/4-1/7
=31/28
追问
最后一题好像不对
追答
1/2+1/6+1/12+1/20+1/30+1/42
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
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