已知数列{an}满足a1=4,an+1=an+p.3^n+1(n属于N+,P为常数）,a1,a2+6,a3成等差数列.（1）求p的值及数列{an}的通项公式.(2)设数列{bn}满足bn=n^2/(an-n),证明：bn

已知数列{an}满足a1=4,an+1=an+p.3^n+1(n属于N+,P为常数）,a1,a2+6,a3成等差数列.（1）求p的值及数列{an}的通项公式.(2)设数列{bn}满足bn=n^2/(an-n),证明：bn
已知数列{an}满足a1=4,an+1=an+p.3^n+1(n属于N+,P为常数）,a1,a2+6,a3成等差数列.
（1）求p的值及数列{an}的通项公式.
(2)设数列{bn}满足bn=n^2/(an-n),证明：bn<=4/9.

已知数列{an}满足a1=4,an+1=an+p.3^n+1(n属于N+,P为常数）,a1,a2+6,a3成等差数列.（1）求p的值及数列{an}的通项公式.(2)设数列{bn}满足bn=n^2/(an-n),证明：bn
经化简得a1 a2 a3 分别为a1=4 a2=a1+3p+1=5+3p  a3=a1+12p+2=6+12p
a1,a2+6,a3成等差数列.
的2a2+12=a1+a3 即22+6p=10+12p 解得p=2
a(n+1)=an+2*3^n+1

a2-a1=2*3^1+1

a3-a2=2*3^2+1

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an-a(n-1)=2*3^(n-1)+1

将这些式子全加起来 得
an-a1=3^n-3+n-1
an=3^n+n
∴bn=n^2/(an-n)=n^2/3^n
另f(x)=x^2/3^x   f'(x)=(2x*3^x-ln3*3^x*x^2)/3^2x
  令f'(x)=0   得1<x1<2
即f(x)在(0,x1)上为增 在(x1,+无穷)为减
f(1)=1/3  f(2)=4/9 显然f(1)<f(2)
即f(x)max=f(2)=4/9  x∈N+
所以bn(max)=b2=4/9
∴bn≤4/9