1/3+1/15+1/35+1/63+.+1/323=1/2(1/1-1/3+1/3-1/5+1/5-1/7+...+1
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/06/24 07:08:48
1/3+1/15+1/35+1/63+.+1/323=1/2(1/1-1/3+1/3-1/5+1/5-1/7+...+1/17-1/19)=1/2(1-1/19)=9/19
1/2哪来的,1/1哪儿来的?怎么抵消的?
1/2哪来的,1/1哪儿来的?怎么抵消的?
1/3+1/15+1/35+1/63+.+1/323
=1/2(2/3+2/15+2/35+2/63+.+2/323)
=1/2[2/(1X3)+2/(3X5)+2/(5X7)+2/(7X9)+.+2/(17X19)]
=1/2[(3-1)/(1X3)+(5-3)/(3X5)+(7-5)/(5X7)+(9-7)/(7X9)+.+(19-17)/(17X19)]
=1/2[3/(1X3)-1/(1X3)+5/(3X5)-3/(3X5)+7/(5X7)-5/(5X7)+9/(7X9)-7/(7X9)+.+19/(17X19)-17/(17X19)]
=1/2(1/1-1/3+1/3-1/5+1/5-1/7+...+1/17-1/19) (1/2和1/1就这样来的)
(括号中第二项和第三项抵消,第四项和第五项抵消.)
=1/2(1-1/19)
=9/19
=1/2(2/3+2/15+2/35+2/63+.+2/323)
=1/2[2/(1X3)+2/(3X5)+2/(5X7)+2/(7X9)+.+2/(17X19)]
=1/2[(3-1)/(1X3)+(5-3)/(3X5)+(7-5)/(5X7)+(9-7)/(7X9)+.+(19-17)/(17X19)]
=1/2[3/(1X3)-1/(1X3)+5/(3X5)-3/(3X5)+7/(5X7)-5/(5X7)+9/(7X9)-7/(7X9)+.+19/(17X19)-17/(17X19)]
=1/2(1/1-1/3+1/3-1/5+1/5-1/7+...+1/17-1/19) (1/2和1/1就这样来的)
(括号中第二项和第三项抵消,第四项和第五项抵消.)
=1/2(1-1/19)
=9/19
已知(1/3-1/5)*1/2=1/15,(1/5-1/7)*1/2=1/35,(1/7-1/9)*1/2=1/63
计算1/3+1/15+1/35+1/63+1/99+1/143+1/195+255+1/323+1/399
1+1/15+3+1/35+5+1/63+7+1/99+9+1/143+11+1/195=?
1/3+1/15+1/35+1/63+1/99.1/323 怎么算
已知(1/3-1/5)×1/2=1/15,(1/5-1/7) ×1/2,(1/7-1/9)1/2+1/63……
1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255 +1/323+1/399=
1/3+1/15+1/35+1/63+1/99
1\3+1\15+1\35+1\63+1\99
(1+1/15)+(3+1/35)+(5+1/63)+(7+1/99)+(9+1/143)+(11+1/195)
1又1/3+3又1/15+5又1/35+7又1/63+1/99 ...
简算:3/1+15/1+35/1+63/1+99/1+143/1+195/1=?
1/3+1/15+1/35+1/63+1/99+1/145+1/195+1/255