Sn=n^3+2n^2+n+1
n=1
a1=5
an = Sn -S(n-1)
= 3n^2-3n+1 +2(2n-1) +1
=3n^2+n
an = 5 ; n=1
= 3n^2+n ; n>=2
Sn=n(n+1)^2+1
n大于等于2
则an=Sn-S(n-1)
=n(n+1)^2+1-(n-1)n^2-1
=n^3+2n^2+n-n^3+n^2
=3n^2+n
a1=S1=1+2+1+1=4
满足an=3n^2+n
所以an=3n^2+n
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