1/2+1/6+1/20+1/30+1/42+1/56+1/72怎样算简便
问题描述：
1/2+1/6+1/20+1/30+1/42+1/56+1/72怎样算简便
答
原式=(1-1/2)+(1/2-1/3)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9) 然后相消后可知式子只剩1-1/3+1/4-1/9 答案就是29/36
答
题打错了吧..按规律中间还有1/12....
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
=(1-1/2)+(1/2-1/3)+……+(1/7-1/8)+(1/8-1/9) (中间相互抵消）
=1-1/9
=8/9
答
1/2+1/6+1/30+1/42+1/56+1/72
=1/(1*2)+1/(2*3)+1/*(5*6)+1/(6*7)+1/(7*8)+1/(8*9)
=(1-1/2)+(1/2-1/3)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
=1-1/2+1/2-1/3+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1-1/3++1/5-1/9
=(135-45+27-15)/135
=102/135