百度作业网已知数列{an}满足a1+a2+a3+…+nan=n(n+1)(n+2),则{an}的通项公式为an=
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已知数列{an}满足a1+a2+a3+…+nan=n(n+1)(n+2),则{an}的通项公式为an=
a1+2a2+3a3+...+nan=n(n+2)(n+1)
a1+2a2+3a3+...+(n-1)a(n-1)=(n-1)n(n+1)
nan-(n-1)a(n-1)=3n(n+1)
nan=(n-1)a(n-1)+3n(n+1)
n(an+xn²+yn+z)=(n-1)(a(n-1)+x(n-1)²+y(n-1)+z)
nan+xn³+yn²+zn=(n-1)a(n-1)+x(n³-3n²+3n+1)+y(n²-2n+1)+zn-z
nan=(n-1)a(n-1)+(-y-3x+y)n²+(-z+3x-2y+z)n+(x+y-z)
-3x=3,x=-1,3x-2y=3,y=-3,x+y-z=0,z=4
n(an-n²-3n+4)=(n-1)(a(n-1)-(n-1)²-3(n-1)+4)
n(an-n²-3n+4)=1*(a1-1²-3+4)
a1=1*2*3=6
n(an-n²-3n+4)=6
an-n²-3n+4=6/n
an=n²+3n-4+6/n
a1+2a2+3a3+...+(n-1)a(n-1)=(n-1)n(n+1)
nan-(n-1)a(n-1)=3n(n+1)
nan=(n-1)a(n-1)+3n(n+1)
n(an+xn²+yn+z)=(n-1)(a(n-1)+x(n-1)²+y(n-1)+z)
nan+xn³+yn²+zn=(n-1)a(n-1)+x(n³-3n²+3n+1)+y(n²-2n+1)+zn-z
nan=(n-1)a(n-1)+(-y-3x+y)n²+(-z+3x-2y+z)n+(x+y-z)
-3x=3,x=-1,3x-2y=3,y=-3,x+y-z=0,z=4
n(an-n²-3n+4)=(n-1)(a(n-1)-(n-1)²-3(n-1)+4)
n(an-n²-3n+4)=1*(a1-1²-3+4)
a1=1*2*3=6
n(an-n²-3n+4)=6
an-n²-3n+4=6/n
an=n²+3n-4+6/n
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