1⼀6+1⼀12+1⼀20+1⼀30+1⼀42简便运算

1/2+1/6+1/12+1/20+1/30+1/42=?

这样的题目一定是做分母的文章

看1/2=1/(1*2)=1-1/2
1/6=1/(2*3)=1/2-1/3
1/12=1/(3*4)=1/3-1/4
1/20=1/(4*5)=1/4-1/5
1/30=1/(5*6)=1/5-1/6
1/42=1/(6*7)=1/6-1/7
现在再来看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
答案很快就知道了.
注意1/(A*B)这样的式子.A和B相差1个数.A小与B就能化成
1/A-1/B的式子

1/6 + 1/12 + 1/20 + 1/30 + 1/42
= (3-2)/6 + (4-3)/12 + (5-4)/20 + (6-5)/30 + (7-6)/42
= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7
= 1/2 - 1/7
= 7/14 - 2/14
= 5/14

先通分再算
420是他们一种一个公分母，则有
（70+35+21+14+10）/420=5/14

1/2－1/3＋1/3-1/4＋1/4-1/5+1/5-1/6+1/6-1/7
=1/2-1/7
=5/14