1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1/(7*9*11)+1/(9*11*13)+1/(11*13*15)等于多少

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/24 10:14:14
1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1/(7*9*11)+1/(9*11*13)+1/(11*13*15)等于多少1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1

1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1/(7*9*11)+1/(9*11*13)+1/(11*13*15)等于多少
1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1/(7*9*11)+1/(9*11*13)+1/(11*13*15)等于多少

1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+1/(7*9*11)+1/(9*11*13)+1/(11*13*15)等于多少
原式=[1/(3*5)]*[1+1/7]+[1/(7*9)]*[1/5+1/11]+[1/(11*13)]*[1/9+1/15]
=8/(15*7)+16/(15*7*33)+8/(9*11*65)
=[8/(3*5*7)]*[1+2/33]+8/(9*11*65)
=8/99+8/(99*65)
=[8/99]*[1+1/65]
=[8/99]*[66/65]
=16/195