已知数列{an}满足a1+2a2+3a3+...+nan=n(n+1)(2n+1),则该数列an=?
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已知数列{an}满足a1+2a2+3a3+...+nan=n(n+1)(2n+1),则该数列an=?
a1+2a2+3a3+...+nan=n(n+1)(2n+1) ①
a1+2a2+3a3+...+(n-1)a(n-1)=n(n-1)^2 ②
①-②可得:nan=n(n+1)(2n+1)-n(n-1)^2
=n^2+5n
a1+2a2+3a3+...+(n-1)a(n-1)=n(n-1)^2 ②
①-②可得:nan=n(n+1)(2n+1)-n(n-1)^2
=n^2+5n
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