大师作文网数列求和……求解
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数列求和……求解
an=(2-n)/2^(n-1)
= 1/2^(n-2) - n.(1/2)^(n-1)
Sn = a1+a2+...+an
= 4(1- 1/2^n) -S
S = 1.(1/2)^0+2(1/2)^1+...+n(1/2)^(n-1) (1)
(1/2)S = 1.(1/2)^1+2(1/2)^2+...+n(1/2)^n (2)
(1)-(2)
(1/2)S = [1+1/2+...+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 = a1+a2+...+an
= 4(1- 1/2^n) -S
= 4(1- 1/2^n) - [4(1-1/2^n) -2n(1/2)^n]
= 2n(1/2)^n
= 1/2^(n-2) - n.(1/2)^(n-1)
Sn = a1+a2+...+an
= 4(1- 1/2^n) -S
S = 1.(1/2)^0+2(1/2)^1+...+n(1/2)^(n-1) (1)
(1/2)S = 1.(1/2)^1+2(1/2)^2+...+n(1/2)^n (2)
(1)-(2)
(1/2)S = [1+1/2+...+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 = a1+a2+...+an
= 4(1- 1/2^n) -S
= 4(1- 1/2^n) - [4(1-1/2^n) -2n(1/2)^n]
= 2n(1/2)^n