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在个式子中怎么化简出这个结果
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![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在个式子中怎么化简出这个结果](/uploads/image/z/4549855-31-5.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%98%AF%E9%A6%96%E9%A1%B9%E4%B8%BAa1%3D1%2F4%2C%E5%85%AC%E6%AF%94q%3D1%2F4%E7%9A%84%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E8%AE%BEbn%2B2%3D3%28log1%2F4%29an%28n%E2%88%88N%2A%29%2C%E6%95%B0%E5%88%97%7BCn%7D%E6%BB%A1%E8%B6%B3Cn%3Dan%2Abn%E5%9C%A8%E4%B8%AA%E5%BC%8F%E5%AD%90%E4%B8%AD%E6%80%8E%E4%B9%88%E5%8C%96%E7%AE%80%E5%87%BA%E8%BF%99%E4%B8%AA%E7%BB%93%E6%9E%9C)
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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在个式子中怎么化简出这个结果
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
在个式子中
怎么化简出这个结果
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在个式子中怎么化简出这个结果
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)
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