设数列AN满足A1等于1,3(A1+a2+~+AN)=(n+2)an,求通向公式

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 22:25:59
设数列AN满足A1等于1,3(A1+a2+~+AN)=(n+2)an,求通向公式

设数列AN满足A1等于1,3(A1+a2+~+AN)=(n+2)an,求通向公式
设数列AN满足A1等于1,3(A1+a2+~+AN)=(n+2)an,求通向公式

设数列AN满足A1等于1,3(A1+a2+~+AN)=(n+2)an,求通向公式
an=n(n+1)/2
3(a1+a2+……+an)=(n+2)an
3Sn = (n+2)an .(1)
3S(n-1) = (n + 1)a(n-1).(2)
(1)-(2)得:
3an = (n+2)an - (n + 1)a(n-1)
(n-1)an = (n + 1)a(n-1)
an/a(n-1) = (n + 1)/(n-1)
然后用你们肯定学过的累乘法:
(a2/a1)(a3/a2)(a4/a3).[a(n-1)/a(n-2)][an/a(n-1)] = (3/1)(4/2)(5/3).[n/(n-2)][(n+1)/(n-1)]
an/a1 = n(n+1)/2
因为a1=1
所以,an = n(n+1)/2

设数列AN满足A1等于1,3(A1+a2+~+AN)=(n+2)an,求通向公式 设数列{an}满足lg(1+a1+a2+...+an)=n+1,求通项公式an 设数列【an】满足a1=1,3(a1+a2+a3+······+an)=(n+2)an,求通项an 设数列{an}满足a1+2a2+3a3+.+nan=n(n+1)(n+2)求通项an 已知数列{an}满足:a1=1,an=a1+2a2+3a3+``````+(n-1)a(n-1)(n大于等于2),则通项公式an是什么? 数列{An}满足a1=1/2,a1+a2+..+an=n方an,求an 【高中数学数列】已知数列an满足a1=1,a2=2,且an=an-1/an-2 (n大于等于3)则a2012=? 设数列{An}满足A1+3A2+3²A3+…+3n-1An=3/n.(1)求数列{An}的通项. 设数列{an}满足a1+3a2+3平方a3+...+3n-1an=n/3,n属于N*.求数列{an}的通项公式? 设数列an满足a1+3a2+3²a3+…+3^n-1(an)=n/3,求数列an的通项公式 数学 如果数列{an}满足a1,a2-a1,a3-a2,……,an-an-1是首项为1,公比为2的等比数列,那么an等于?求大神 若数列{an}满足a1,a2-a1,a3-a2,...是以1为首相,3为公比的等比数列,则an______ 数列{an}满足a1,a2/a1,a3/a2,…an/an-1…是首项为1,公比为2的等比数列,则a100等于? 如果数列{an}满足a1,a2/a1,a3/a2,...an/an-1,...是首项为1,公比为2的等比数列,则a101等于() 设数列{An}满足 A1=6,A2=4 A3=3,且数列{An+1-An}(n属于自然数)是等差数列,球An的通向公式 rt设数列{An}满足 A1=6,A2=4 A3=3,且数列{An+1-An}(n属于自然数)是等比数列,球An的通向公式rt 已知数列{an}满足条件:a1=5,an=a1+a2+...a(n-1) n大于等于2,求数列{an}的通项公式 数列{an}满足a1=3/2,an+1=an2-an+1,求证:1/an=1/(an)-1 - 1/(an+1)-1数列{an}满足a1=3/2,an+1=an2-an+1,求证:1/an=1/(an)-1 - 1/(an+1)-1设Sn=1/a1+1/a2+...+1/an,n>2证明1 数列{an}满足:1/a1+2/a2+3/a3+…+n/an=2n(1)求通项公式an(2)设Sn=a1+a2+…+an,求1/S1+2/S2+…+n/Sn