对于等差数列除以等比数列前n项和的求解设等差数列An=2-n,等比数列Bn=2^(n-1),求数列An/Bn的前n项和.求助啊!

来源：学生作业帮助网编辑：作业帮时间：2024/05/05 09:25:55

对于等差数列除以等比数列前n项和的求解设等差数列An=2-n,等比数列Bn=2^(n-1),求数列An/Bn的前n项和.求助啊!
对于等差数列除以等比数列前n项和的求解
设等差数列An=2-n,等比数列Bn=2^(n-1),求数列An/Bn的前n项和.求助啊!

对于等差数列除以等比数列前n项和的求解设等差数列An=2-n,等比数列Bn=2^(n-1),求数列An/Bn的前n项和.求助啊!
Sn=1*(1/2)^0+0*(1/2)^1 +(-1)*(1/2)^2+(-2)*(1/2)^3 +……+(2-n)(1/2)^(n-1).①
(1/2)Sn= 1*(1/2)^1 +0*(1/2)^2 +(-1)*(1/2)^3 +(-2)*(1/2)^4+……+(2-n)(1/2)^n.②
①-②
(1/2)Sn=1*(1/2)^0+(-1)*(1/2)^1 +(-1)*(1/2)^2+(-1)*(1/2)^3 +……+(-1)(1/2)^(n-1)+(n-2)(1/2)^n
=1-[ (1/2)^1 +(1/2)^2+(1/2)^3 +……+(1/2)^(n-1) ] + (n-2)(1/2)^n
=1-[1-2^(1-n)] + (n-2)/2^n
=1/2^(n-1) +(n/2 -1)/2^(n-1)
=(n/2)/2^(n-1)
=n/2^n
Sn=2n/2^n = n / 2^(n-1) 即：Sn = n / 2^(n-1)

对于等差数列除以等比数列前n项和的求解设等差数列An=2-n,等比数列Bn=2^(n-1),求数列An/Bn的前n项和.求助啊! 等差数列除以等比数列 an=n bn=2^n-3 求an除以bn的前n项和设Sn是等比数列的前n项和,S3,S9,S6成等差数列求证a2,a8,a5成等差数列等差数列、等比数列前n项和公式? 证明等差数列,等比数列前n项和的公式设Sn是等比数列{an}的前n项和,S3,S9,S6,成等差数列,则公比q=? 设等差数列An的前n项和为Sn,则S4,S8-S4,S12-S8,S16-S12成等差数列,类比以上结论有设等比数列Bn的前n项积为Tn,则T4,,,T16/T12成等比数列等差数列前n项和的公式是什么?等比数列前n项和的公式是什么? 证明,设公比不为1的等比数列{an}的前n项和为Sn,a2,a4,a3成等差数列,则S2,S4,S3成等差数列设Sn是等比数列an的前n项和S3.S9.S6成等差数列,求a3.a9.a6成等差数列设Sn是等比数列an的前n项和S3.S9.S6成等差数列,求a3.a9.a6成等差数列设Sn是等比数列｛an｝的前n项和,s3,S9,S6,成等差数列求证:a2,a8,a5　成等差数列设Sn是等比数列｛an｝的前n项和,s3,s9,s6,成等差数列求证:a2,a8,a5　成等差数列设等比数列an的公比q=2,前n项和为sn,则s4除以a2= 设等比数列an的公比为q,前n项和为sn,若s(n+1),sn,s(n+2)成等差数列,求q的值设等比数列[an]的公比为q,前n项和为Sn,若S(n+1),Sn,S(n+2)成等差数列,则q的值? 已知等比数列Bn=2^n,等差数列An=3n+1,设Cn=An*Bn,求Cn的前n项和Sn. 设等比数列｛an｝的公比为q,前n项和为Sn,若S(n+1),Sn,S(n+2)成等差数列,则q=