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2/5+2/45+2/117+2/221=?

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/05 14:15:45
2/5+2/45+2/117+2/221=?
2/5+2/45+2/117+2/221
=(1-1/5)/2+(1/5-1/9)/2+(1/9-1/13)/2+(1/13-1/17)/2
=[(1-1/5)+(1/5-1/9)+(1/9-1/13)+(1/13-1/17)]/2
=(1-1/17)/2
=8/17
再问: 灾情问这位大虾: 33又8/11 * 49又61/62 + 28又3/11 * 159又61/62 =? 乘号用 * 代替 (1+1/3)*(1+1/9)*(1+1/81)=? 1 + 3又1/6 + 5又1/12 + 7又1/20 + 9又1/30 + 11又1/42=? 1 + 1/(1+2) + 1/(1+2+3) + ..... +1/(1+2+3+4+5+6+7+8+9+10)=?
再答: 第一题没看明白 (1+1/3)*(1+1/9)*(1+1/81) =(1-1/3)(1+1/3)*(1+1/9)*(1+1/81)/(1-1/3) 利用平方差公式 =(1-1/81²)*3/2 =(81²-1)/81² *3/2=....... 1 + 3又1/6 + 5又1/12 + 7又1/20 + 9又1/30 + 11又1/42=? =(1+3+5+7+9+11)+(1/6+1/12+1/20+1/30+1/42) =36+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7) =36+1/2-1/7 =36又5/14 1 + 1/(1+2) + 1/(1+2+3) + ..... +1/(1+2+3+4+5+6+7+8+9+10) =1/1+1/3+1/6+1/10+....+1/45 =2(1/2+1/6+1/12+1/20.....+1/90) =2(1-1/2+1/2-1/3+1/3-1/4+....+1/9-1/10) =2*(1-1/10) =9/5