神马作文网解照片中关于数列的题
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/19 15:42:25
解照片中关于数列的题
(1)
a1+2a2+...+2^(n-1)an =n/2 (1)
n=1,a1=1/2
a1+2a2+...+2^(n-2)a(n-1) =(n-1)/2 (2)
(1)-(2)
2^(n-1)an = 1/2
an = 1/2^n
(2)
bn=(2n-1)an
=(2n-1)(1/2^n)
= n.(1/2)^(n-1) - 1/2^n
Sn = b1+b2+...+bn
= S - (1- 1/2^n)
S = 1.(1/2)^0 + 2.(1/2)^1+...+n(1/2)^(n-1) (3)
(1/2)S = 1.(1/2)^1 + 2.(1/2)^2+...+n(1/2)^n (4)
(1)-(2)
(1/2)S = [1+1/2+1/2^2+...+1/2^(n-1)] -n(1/2)^n
= 2(1-1/2^n) -n(1/2)^n
S = 4(1-1/2^n) -2n(1/2)^n
Sn = b1+b2+...+bn
= S - (1- 1/2^n)
=4(1-1/2^n) -2n(1/2)^n - (1- 1/2^n)
= 3 - (2n+3)(1/2)^n
a1+2a2+...+2^(n-1)an =n/2 (1)
n=1,a1=1/2
a1+2a2+...+2^(n-2)a(n-1) =(n-1)/2 (2)
(1)-(2)
2^(n-1)an = 1/2
an = 1/2^n
(2)
bn=(2n-1)an
=(2n-1)(1/2^n)
= n.(1/2)^(n-1) - 1/2^n
Sn = b1+b2+...+bn
= S - (1- 1/2^n)
S = 1.(1/2)^0 + 2.(1/2)^1+...+n(1/2)^(n-1) (3)
(1/2)S = 1.(1/2)^1 + 2.(1/2)^2+...+n(1/2)^n (4)
(1)-(2)
(1/2)S = [1+1/2+1/2^2+...+1/2^(n-1)] -n(1/2)^n
= 2(1-1/2^n) -n(1/2)^n
S = 4(1-1/2^n) -2n(1/2)^n
Sn = b1+b2+...+bn
= S - (1- 1/2^n)
=4(1-1/2^n) -2n(1/2)^n - (1- 1/2^n)
= 3 - (2n+3)(1/2)^n