数列Cn的前n项和Tn?

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数列Cn的前n项和Tn?
数列Cn的前n项和Tn?
 

数列Cn的前n项和Tn?
cn = (3n-1)/2^n
= 3(n.1/2^n) - 1/2^n
Tn = c1+c2+...+cn
=3S - (1-1/2^n)
S = 1.(1/2)^1+2.(1/2)^2+...+n.(1/2)^n (1)
(1/2)S = 1.(1/2)^2+2.(1/2)^3+...+n.(1/2)^(n+1) (2)
(1)-(2)
(1/2)S = (1/2+1/2^2+.+1/2^n) - n.(1/2)^(n+1)
= (1-1/2^n) -n.(1/2)^(n+1)
S = 2 - (n+2)(1/2)^n
Tn = 3S - (1-1/2^n)
= 6 - 3(n+2)(1/2)^n - (1-1/2^n)
= 5 -(3n+5)(1/2)^n