设数列{bn}满足b1=3,bn=3^nP^n,且Pn+1=Pn+n/3^n+1,若存在实数t,使得数列Cn=[bn-(1/4)]*t/(n+1)+n成等差数列,记数列{Cn*(1/2)^Cn}的前n项和为Tn.证明:3^n*(Tn-1)<bn
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![设数列{bn}满足b1=3,bn=3^nP^n,且Pn+1=Pn+n/3^n+1,若存在实数t,使得数列Cn=[bn-(1/4)]*t/(n+1)+n成等差数列,记数列{Cn*(1/2)^Cn}的前n项和为Tn.证明:3^n*(Tn-1)<bn](/uploads/image/z/12080545-25-5.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97%7Bbn%7D%E6%BB%A1%E8%B6%B3b1%3D3%2Cbn%3D3%5EnP%5En%2C%E4%B8%94Pn%2B1%3DPn%2Bn%2F3%5En%2B1%2C%E8%8B%A5%E5%AD%98%E5%9C%A8%E5%AE%9E%E6%95%B0t%2C%E4%BD%BF%E5%BE%97%E6%95%B0%E5%88%97Cn%3D%5Bbn-%EF%BC%881%2F4%EF%BC%89%5D%2At%2F%28n%2B1%29%2Bn%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E8%AE%B0%E6%95%B0%E5%88%97%7BCn%2A%281%2F2%29%5ECn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BATn.%E8%AF%81%E6%98%8E%EF%BC%9A3%5En%2A%28Tn-1%29%EF%BC%9Cbn)
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