数列{An}中,若An=（3n-2）x（1/4）n次方.求数列的前n项和Sn

数列{An}中,若An=（3n-2）x（1/4）n次方.求数列的前n项和Sn
数列{An}中,若An=（3n-2）x（1/4）n次方.求数列的前n项和Sn

数列{An}中,若An=（3n-2）x（1/4）n次方.求数列的前n项和Sn

a(n) = (3n-2)/4^n,
s(n) = a(1) + a(2) + a(3) + ... + a(n-1) + a(n)
= (3*1-2)/4 + (3*2-2)/4^2 + (3*3-2)/4^3 + ... + [3(n-1)-2]/4^(n-1) + (3n-2)/4^n,
4s(n) = (3*1-2) + (3*2-2)/4 + (3*3-2)/4^...

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a(n) = (3n-2)/4^n,
s(n) = a(1) + a(2) + a(3) + ... + a(n-1) + a(n)
= (3*1-2)/4 + (3*2-2)/4^2 + (3*3-2)/4^3 + ... + [3(n-1)-2]/4^(n-1) + (3n-2)/4^n,
4s(n) = (3*1-2) + (3*2-2)/4 + (3*3-2)/4^2 + ... + [3(n-1)-2]/4^(n-2) + (3n-2)/4^(n-1),
3s(n) = 4s(n) - s(n) = (3*1-2) + 3/4 + 3/4^2 + ... + 3/4^(n-1) - (3n-2)/4^n
= 3[1 + 1/4 + 1/4^2 + ... + 1/4^(n-1)] - 2 - (3n-2)/4^n
= 3[ 1 - 1/4^n]/(1-1/4) - 2 - (3n-2)/4^n
= 4[ 1- 1/4^n] - 2 - (3n-2)/4^n
= 4 - 4/4^n - 2 - (3n-2)/4^n
= 2 - (3n+2)/4^n,
s(n) = 2/3 - (1/3)(3n+2)/4^n

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