Question

已知数列an满足a1+2a2+3a3+……nan=n(n+1)(n+2)求an

Answer 1

数列nan的前n项和为n（n+1）（n+2），根据sn求an ，会否

Answer 2

∵a1+2a2+3a3+……+nan=n(n+1)(n+2)…………①
∴a1+2a2+3a3+……+(n-1)a(n-1)=(n-1)n(n+1)…………②

①-②得
nan=n(n+1)(n+2)-(n-1)n(n+1)
=[(n+2)-(n-1)]n(n+1)
=3n(n+1)
∴an=3(n+1)

Answer 3

Answer 4

a1+2a2+3a3+...+nan=n(n+1)(n+2)..............①
a1+2a2+3a3+...+(n-1)an-1=(n-1)n(n+1)........②
①-②得：nan=n(n+1)(n+2)-(n-1)n(n+1)=n(n+1)(n+2-n+1)=3n(n+1)
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