数列{an}满足a1+2a2+3a3+…+n(n+1)(n+2),求数列{an}的通项公式.

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数列{an}满足a1+2a2+3a3+…+n(n+1)(n+2),求数列{an}的通项公式.

数列{an}满足a1+2a2+3a3+…+n(n+1)(n+2),求数列{an}的通项公式.
数列{an}满足a1+2a2+3a3+…+n(n+1)(n+2),求数列{an}的通项公式.

数列{an}满足a1+2a2+3a3+…+n(n+1)(n+2),求数列{an}的通项公式.
隐函数关系
a1+2a2+3a3+…+(n-1)a(n-1)+nan=n(n+1)(n+2)
a1+2a2+3a3+…+(n-1)a(n-1)=(n-1)(n-1+1)(n-1+2)=(n-1)n(n+1) n>=2
相减得nan=n(n+1)(n+2-n+1)=3n(n+1) n>=2
an=3(n+1) n>=2
a1=6也符合.故an=3(n+1)

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