已知an满足a1=三分之二 an+1=an-2/2an-3 求证1/an-1是等差数列
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/10/01 03:31:19
已知an满足a1=三分之二 an+1=an-2/2an-3 求证1/an-1是等差数列
如题
如题
证:
a(n+1)=(an -2)/(2an -3)
a(n+1) -1=(an-2-2an+3)/(2an-3)=(-an+1)/(2an-3)=-(an -1)/(2an-3)
1/[a(n+1) -1]=-(2an -3)/(an -1)=1/(an -1) -2
1/[a(n+1)-1]-1/(an -1)=-2,为定值.
1/(a1-1)=1/(2/3 -1)=-3
数列{1/(an -1)}是以-3为首项,-2为公差的等差数列.
a(n+1)=(an -2)/(2an -3)
a(n+1) -1=(an-2-2an+3)/(2an-3)=(-an+1)/(2an-3)=-(an -1)/(2an-3)
1/[a(n+1) -1]=-(2an -3)/(an -1)=1/(an -1) -2
1/[a(n+1)-1]-1/(an -1)=-2,为定值.
1/(a1-1)=1/(2/3 -1)=-3
数列{1/(an -1)}是以-3为首项,-2为公差的等差数列.
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,An+1=2An+2^n.求证数列An/2是等差数列
已知数列an满足an+1=3an/an+3求证{1/an}是等差数列.当a1=1/2时求a100
已知数列{an}满足2an/an+2=an+1(n属于正整数),a1=1/1006.求证:数列{1/an}是等差数列,并
已知数列{an}满足a1=2,an+1=2an/an+2.求证数列{1/an}是否为等差数列 并求出an
已知数列{an}满足a1=2,a(n+1)=(3an-2)/(2an-1),求证{1/(an-1)}是等差数列,并求数列
已知数列{an}满足an+1=(3an+1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an
已知数列{an}满足a1=4,an=4-4/an-1(n>=2),设bn=1/an-2(1)求证{bn}是等差数列;(2
已知数列{an}满足an+an+1=2n+1(n∈N*),求证:数列{an}为等差数列的充要条件是a1=1.
已知数列an满足a1=4 an=4-4/an-1(n大于等于2) 求证bn是等差数列 求数列an的通项公式
已知a1=1,2an+1*an+3an+1+an+2=0 求证{1/an+1}为等差数列(2)求an
数列{an}满足a1=1,an=an-1(1+2an)(n-1是下标).1、求证:{1/an}是等差数列;2、若a1a2