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1又1/2+2又1/6+3又1/12+4又1/20+5又1/30+6又1/42+7...

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1又1/2+2又1/6+3又1/12+4又1/20+5又1/30 =(1+2+3+4+5)+(1/2+1/6+1/12+1/20+1/30) =5*6/2+((1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)) =15+(1-1/6) =15+5/6 =95/6

我觉得直接计算后两者相加,再向前加就可以,很简便 望采纳

原式=(1+2+3+...+9)+(1/6 +1/12+1/20+...+1/90) =45+[1/(2×3)+1/(3×4)+1/(4×5)+...+1/(9×10)] =45+1/2 -1/3 +1/3 -1/4+ 1/4 -1/5+...+1/9 -1/10 =45+ 1/2 -1/10 =45又5分之2

二又3/20-(5/6-1/12) =2+3/20+1/12-5/6 =2-(50/60-9/60-5/60) =2-36/60 =2-3/5 =1又5分之2

原式=2+3+1/6+5+1/12+7+1/20+11+1/30+13+1/42=2+3+5+7+11+13+1/6+1/12+1/20+1/30+1/42=41+10/60+5/60+3/60+2/60+1/42=41+(10+5+3+2)/60+1/42=41+20/60+1/42=41+1/3+1/42=41+14/42+1/42=41+15/42=41+5/14 结果为41又5/14

原式 =1-2-3-4+5-6+7-8+9+1/2-5/6-1/12-9/20+1/30-1/42+1/56-71/72+1/90 =-1+1-1/2-1+1/2-1/3-1/3+1/4-1/2+1/4-1/5+1/5-1/6-1/6+1/7+1/7-1/8-1+1/8-1/9+1/9-1/10 =-2-2/3-1/2+1/2-1/3+2/7-1/10 =-3+2/7-1/10 =-3+(20-7)/70 =-3+13/70 =-2又57/70

1+1又1/2+5/6+7/12+9/20+11/30(简便计算) =2又1/2+1/2+1/3+1/3+1/4+1/4+1/5+1/5+1/6 =3+2/3+1/2+2/5+1/6 =3+2/3+(1/2+1/6)+2/5 =3+2/3+2/3+2/5 =4又1/3+2/5 =4又5/15+6/15 =4又11/15

1又20分之1加上2又30分之1加上3又42分之1加上4又56分之1加上5又72分之1加上6又90分之1加上7又110分之1加上8又132分之1 =(1+2+3+4+5+6+7+8)+(1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132) ‍ =36+(1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+...

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