数列An满足An+1=An(1—An+1),A1=1,数列Bn=AnA(n+1),则数列Bn的前10项的和=

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/16 20:30:10
数列An满足An+1=An(1—An+1),A1=1,数列Bn=AnA(n+1),则数列Bn的前10项的和=
x){6uӎyv/|mccᣆ) DSPQ,c&L/1'$`;(O:^꘧ Q`';ط鄞3UeVx  yw_.tȓ uy}Pk;A$FA 2^?fp,H 4`>ȡF@ 16y԰

数列An满足An+1=An(1—An+1),A1=1,数列Bn=AnA(n+1),则数列Bn的前10项的和=
数列An满足An+1=An(1—An+1),A1=1,数列Bn=AnA(n+1),则数列Bn的前10项的和=

数列An满足An+1=An(1—An+1),A1=1,数列Bn=AnA(n+1),则数列Bn的前10项的和=
An+1=An(1—An+1)
所以An-An+1=AnAn+1
两边同除以AnAn+1
则1/An+1-1/An=1
所以数列｛1/An｝是首项为1,公差是1的等差数列
所以1/An=n
即An=1/n
则Bn=1/[n(n+1)]=1/n-1/(n+1)
所以Bn的前10项的和=1-1/2+1/2-1/3+1/3-1/4……+1/10-1/11=1-1/11=10/11

已知数列{an}满足a1=1 an+1=an/(3an+1) 则球an 已知数列{an}中满足(An+1-An)(An+1+An)=16,且a1=1,an 数列{an}满足a1=1 an+1=2n+1an/an+2n 已知数列{an}满足an+1=an+n,a1等于1,则an=? 数列｛an｝满足a1=1,且an=an-1+3n-2,求an 数列an满足a1=2,an+1=4an+9,则an=? 已知数列{an}满足an+1=2an+3.5^n,a1=6.求an 数列{An}满足a1=1/2,a1+a2+..+an=n方an,求an 数列an满足a1=2,an+1=an²求an 数列an满足a1=2,an+1=an²求an 数列[An]满足An+1-An+3=0,且A1=-5.求An. 数列{an}满足an=p/(pn+1-p)(0 已知数列an满足 a1=1/2,an+1=3an/an+3求证1/an为等差数列已知数列an满足 a1=1/2,an+1=3an/an+3求证1/an为等差数列 已知数列an满足a1=1,1/an+1=根号1/an^2+2,an>0,求an 数列{an}满足:a1=1,an>0,an+1^2-an^2=1,那么an 已知数列｛an｝满足a1=1,an+1 -an+2an+1•an=0求通项 数列{an}满足:a1=1,an>0,an+1^2-an^2=1,那么an 已知数列{an}满足a1=1,a2=3,an+2=3an+1-2an求an