两个数列{an}和{bn}满足bn=a1+2a2+...+nan/1+2+...+n,求证:若{bn}为等差数列,则数列{an}也是等差数列?能看懂的

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 01:32:49
两个数列{an}和{bn}满足bn=a1+2a2+...+nan/1+2+...+n,求证:若{bn}为等差数列,则数列{an}也是等差数列?能看懂的

两个数列{an}和{bn}满足bn=a1+2a2+...+nan/1+2+...+n,求证:若{bn}为等差数列,则数列{an}也是等差数列?能看懂的
两个数列{an}和{bn}满足bn=a1+2a2+...+nan/1+2+...+n,求证:若{bn}为等差数列,则数列{an}也是等差数列?
能看懂的

两个数列{an}和{bn}满足bn=a1+2a2+...+nan/1+2+...+n,求证:若{bn}为等差数列,则数列{an}也是等差数列?能看懂的
设Bn公差为d
Bn=(A1+2A2+3A3+……+nAn)/(1+2+3+……+n)
=2(A1+2A2+3A3+……+nAn)/[n(n+1)][分子分母同时乘(n+2)]
=2(A1+2A2+3A3+……+nAn)(n+2)/[n(n+1)(n+2)]
B(n+1)=[A1+2A2+3A3+……+nAn+(n+1)A(n+1)]/[1+2+3+……+n+(n+1)]
=2[A1+2A2+3A3+……+nAn+(n+1)A(n+1)]/[(n+1)(n+2)][分子分母同时乘n]
=2[A1+2A2+3A3+……+nAn+(n+1)A(n+1)]n/[n(n+1)(n+2)]
由Bn+d=B(n+1),得
2n(A1+2A2+3A3+……+nAn)+4(A1+2A2+3A3+……+nAn)+n(n+1)(n+2)d=
2n(A1+2A2+3A3+……+nAn)+2n(n+1)A(n+1)
4(A1+2A2+3A3+……+nAn)+n(n+1)(n+2)d=2n(n+1)A(n+1)……1式
用n-1代换n,得
4(A1+2A2+3A3+……+(n-1)A(n-1))+(n-1)n(n+1)d=2n(n-1)An……2式
1式-2式,得
4nAn+3n(n+1)d=2n(n+1)A(n+1)-2n(n-1)An
2n(n+1)An+3n(n+1)d=2n(n+1)A(n+1)
An+1.5d=A(n+1)

两个数列{an}和{bn}满足bn=a1+2a2+...+nan/1+2+...+n,求证:若{bn}为等差数列,则数列{an}也是等差数列?能看懂的 数列{an}中,a1=-60,an+1=an+3,若数列{bn}满足bn=|an|,求数列{bn}前30项和 数列an,bn满足a1=b1=1,an+1-an=bn+1/bn=2,则数列ban的前10项和为 两个数列{an}和{bn}满足bn=a1+2a2+...+nan/1+2+...+n,若{an}为等差数列,则数列{bn}也是等差数列?要求不能利用1的平方加上2的平方等下去公式的那种 已知数列{an}和{bn}满足关系:bn=(a1+a2+a3+…+an)/n,(n∈N*).若{bn}是等差数列,求证{an}为等差数列 设各项均为正数的数列{an}和{bn}满足:an,bn,an+1成等差数列,bn,an+1,bn+1等比数列且a1=1,b1=2,a2=3求通项an,bn 设各项均为正数的数列{an}和{bn}满足:an,bn,an+1成等差数列,bn,an+1,bn+1成等比数列,且a1=1,b1=2,a2=3,求通项an,bn 已知数列{an}、{bn}满足:a1=1/4,an+bn=1,bn+1=bn/1-an^2.求{bn}通项公式 已知数列{an},{bn}满足a1=2,2an=1+ana(n+1),bn=an-1,设数列{bn}的前n项和为Sn,Tn=S2n-Sn.求数列{bn}的通项公式. 数列an中,a1=3,an=(3an-1-2)/an-1,数列bn满足bn=an-2/1-an,证明bn是等比数列 2.求数列an通项公式和最大项3求liman 已知数列an满足an=31-6n,数列bn满足bn=(a1+a2+...+an)/n,求数列bn的前20项之和. 两个数列{an}和{bn}满足bn=a1+2a2+3a3+.+nan1+2+3+...+n (n€N+). ① 若{b}是等差数列,求证{a}也是等两个数列{an}和{bn}满足bn=a1+2a2+3a3+.+nan/1+2+3+...+n (n€N+).① 若{b}是等差数列,求证{a}也是等差数列② 已知数列{an}、{bn}满足:a1=1/4,an+bn=1,bn+1=bn/1-an^2 (1)求{an}的通项公式 设各项均为正数的数列{an}和{bn}满足5^[an ],5^[bn] ,5^[a(n+1)] .设各项均为正数的数列{an}和{bn}满足5^[an ],5^[bn] ,5^[a(n+1)] 成等比数列,lg[bn],lg[a(n+1)],lg[bn+1]成等差数列,且a1=1,b1=2,a2=3,求通项an、bn. 已知数列{an},{bn}满足a1=2,2an=1+2an*an+1,设{bn}=an-1求数列{1n}为等差数列急!!! 已知数列{an}满足an+Sn=n,数列{bn}满足b1=a1,且bn=an-a(n-1),(n≥2),试求数列{bn}的前n项的和Tn 已知数列an满足a1=2 其前n项和为Sn Sn =n+7~3an 数列bn满足 bn=an~1 证明数列bn是等差数列 已知数列{an},{bn}满足a1=b1=1,an-1-an=bn+1/bn=2求{Ban}和[an/bn}的前n项和