已知an=(3n-1)(3n+2)(1-n)求an的前n项和Tn.

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已知an=(3n-1)(3n+2)(1-n)求an的前n项和Tn.
已知an=(3n-1)(3n+2)(1-n)求an的前n项和Tn.

已知an=(3n-1)(3n+2)(1-n)求an的前n项和Tn.
an=(3n-1)(3n+2)(1-n)=(9n^2+3n-3)(1-n)=-9n^3+6n^2+5n-2 Tn=-9(1^3+2^2+……+n^3)+6(1^2+2^2+……+n^2)+5(1+2+……+n)-2n =-9(1+2+……+n)^2+n(n+1)(2n+1)+5(1+n)n/2-2n =-9(1+n)^2*n^2/4+n(n+1)(2n+1)+5n(n+1)/2-2n =n(1-n)(9n^2+19n+6)/4