1/2+1/6+1/20+1/30+1/42+1/56+1/72怎样算简便

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1/2+1/6+1/20+1/30+1/42+1/56+1/72怎样算简便
1/2+1/6+1/20+1/30+1/42+1/56+1/72怎样算简便

1/2+1/6+1/20+1/30+1/42+1/56+1/72怎样算简便
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

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

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

2%1+6%1+12%1+20%1+30%1 1/2+1/6+1/12+1/20+1/30 1/2,-1/6,1/12,-1/20,1/30 1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72 1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72 1+1/2+1/12+1/6+1/20+1/30+1/40+1/56 1/2+1/6+1/12+1/20+1/30+1/42+1/56 简算 1/2+1/6+1/12+1/20+1/30+1/42+1/56简算, 简便运算：1/2+1/6+1/12+1/20+1/30+1/42+1/56 1+1/2+1/6+1/12+1/20+1/30+1/42的简便计算 2/1+6/1+12/1+20/1+30/1+42/1+56/1=? 1/2 - 1/6 - 1/12 - 1/20 - 1/30 - 1/42 - 1/56怎么算 1/2+1/6+1/12+1/20+1/30+.1/380+1/420= 1+1/2+1/6+1/12+1/20+1/30+1/42=? 1/2+1/6+1/12+1/20+1/30+1/42+1/56 1/2-1/6-1/12-1/20-1/30-1/42-1/56等于多少 2/1+6/1+12/1+20/1+30/1+42/1+56/1= 1/2+1/6+1/12+1/20+1/30+...+1/9702+1/9900