Question

仔细观察下面的每组算式并计算，看看你能发现什么？

（1）1／2×1／3＝1/6 1/2-1/3＝1/6
(2)1/3×1/4=1/12 1/3-1/4=1/12
。。。。。。
（5）通过计算，你发现了什么规律？

（6）1/2+1/6+1/12+1/20+1/30+1/42=？？？？

本人很急的！！！！！！！！

Answer 1

你好，_枯の茉莉

(5)通过计算，你发现了什么规律？
1/n ×1/(n+1)=1/n-1/(n+1)

(6)
1/2+1/6+1/12+1/20+1/30+1/42
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=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

(5)
1/2=1/1X1/2=1/1-1/2
1/6=1/2X1/3=1/2-1/3
1/12=1/3×1/4=1/3-1/4
.......................................
依次类推，文字描述自己写啊
(6)
1/2+1/6+1/12+1/20+1/30+1/42=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/6-1/7
=1-1/7
=6/7

Answer 3

发现规律为1/a*1/(a+1)=1/a-1/(a+1)

原式=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