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问题: 求数列的通项

数列{An}满足:a1+2a2+3a3+``````+Nan=n(n+1)(n+2),求an.

解答:

a1+2a2+...+Nan=n(n+1)(n+2)
a1+2a2+...+(N-1)a下标n-1=(n-1)n(n+1)
两式作差可得:Nan=3n(n+1),于是an=3(n+1)