帮帮计算

1/6+1/12+1/20+1/30+1/42+1/56+1/72
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
=1/2-1/9
=7/18
总结规律:1/(a*b)(a,b为连续正整数)
则有1/(a+b)=1/a-1/b (遇上这样的题,要自己发现数字特征,然后找规律解题.
更一般地:1/(a*b)(a,b之差为n)
则有1/(a+b)=(1/a-1/b)*(1/n)

6分之1+12分之1+20分之++30分之1+42分之1+56分之1+72分之1
=1/2-1/3+1/3-1/4+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/2-1/9
=7/18
规律你应该看明白吧
把式子分成这样就可以约分

1/6+1/12+1/20+1/30+1/42+1/58+1/72
=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)
=1/2-1/3+1/3-1/4+1/4+1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/2-1/9
=7/18

7/18

7/18

1/6+1/12+1/20+1/30+1/42+1/56+1/72
=[2/12+1/12]+[3/60+2/60]+1/42+1/56+1/72
=1/4+1/12+1/42+1/56+1/72
=[3/12+1/12]+1/42+1/56+1/72
=1/3+1/42+1/56+1/72
=[14/42+1/42]+1/56+1/72
=5/14+1/56+1/72
=[20/56+1/56]+1/72
=3/8+1/72
=27/72+1/72
=28/72=7/18