Question

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=1-1/2
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

Answer 1

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

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

Answer 2

公式：1/n(n+1)=1/n-1/n+1
答案：1-1/7=6/7