已知数列{an}是首项为a1=1/4,公比q=1/4的等比数列,设bn+2=3(log1/4)an(n∈N*),数列{Cn}满足Cn=an*bn
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3/4Sn=1/4+3*[(1/4)^2+(1/4)^3+...+(1/4)^n]-(3n-2)*(1/4)^(n+1) (中括号内的是等比数列)
=1/4+3*(1/4)^2*[1-(1/4)^(n-1)]/(1-1/4)-(3n-2)*(1/4)^(n+1)
=1/4+1/4*[1-(1/4)^(n-1)]-(3n-2)*(1/4)^(n+1)
=1/4+1/4-(1/4)^n-(3n-2)*(1/4)^(n+1)
=1/2-4*(1/4)^(n+1)-(3n-2)*(1/4)^(n+1)
=1/2-(4+3n-2)*(1/4)^(n+1)
=1/2-(3n+2)*(1/4)^(n+1)
=1/4+3*(1/4)^2*[1-(1/4)^(n-1)]/(1-1/4)-(3n-2)*(1/4)^(n+1)
=1/4+1/4*[1-(1/4)^(n-1)]-(3n-2)*(1/4)^(n+1)
=1/4+1/4-(1/4)^n-(3n-2)*(1/4)^(n+1)
=1/2-4*(1/4)^(n+1)-(3n-2)*(1/4)^(n+1)
=1/2-(4+3n-2)*(1/4)^(n+1)
=1/2-(3n+2)*(1/4)^(n+1)
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