数列An 满足 a1+2a2+3a3+.+nan=n(n+1)(n+2) 求an

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数列An 满足 a1+2a2+3a3+.+nan=n(n+1)(n+2) 求an
数列An 满足 a1+2a2+3a3+.+nan=n(n+1)(n+2) 求an

数列An 满足 a1+2a2+3a3+.+nan=n(n+1)(n+2) 求an
a1+2a2+3a3+.+nan=n(n+1)(n+2),
a1+2a2+3a3+.+nan+(n+1)a(n+1)=(n+1)(n+2)(n+3).
两式相减,得到(n+1)a(n+1)=(n+1)(n+2)(n+3)-n(n+1)(n+2),故a(n+1)=(n+2)(n+3)-n(n+2)=3(n+2),即有an=3(n+1) (n>=2)
此外,n=1时,a1=1*2*3=6.

a1+2a2+....+nan=n(n+1)(n+2)
a1+2a2+....+nan+(n+1)a(n+1)=(n+1)(n+2)(n+3)
两式相减得
(n+1)a(n+1)=(n+1)(2n+4)
则a(n+1)=2n+4
则an=2n+2

an=n

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