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

网友回答

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.
======以下答案可供参考======
供参考答案1:
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
供参考答案2:
an=n