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