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=

问题描述:

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...