作业帮等差数列中
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等差数列中
等差数列中
等差数列中
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a1=5/6
a(n+1)= (1/3)an + (1/2)^(n+1)
a(n+1) -3(1/2)^(n+1) = (1/3)[an -3(1/2)^n]
{an -3(1/2)^n}是等比数列，q=1/3
an -3(1/2)^n = (1/3)^(n-1).(a1 -3(1/2))
= -2(1/3)...
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a1=5/6
a(n+1)= (1/3)an + (1/2)^(n+1)
a(n+1) -3(1/2)^(n+1) = (1/3)[an -3(1/2)^n]
{an -3(1/2)^n}是等比数列，q=1/3
an -3(1/2)^n = (1/3)^(n-1).(a1 -3(1/2))
= -2(1/3)^n
an =3(1/2)^n -2(1/3)^n
bn= 2^n.an
= 3 - 2(2/3)^n
Sn =b1+b2+...+bn
= 3n - 2[ (2/3)[ 1- (2/3)^n] / (1-2/3) ]
= 3n - 4[ 1- (2/3)^n ]
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