令n=1时,a1=1*2*3=6；依题意：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),从而：an=3(n...