数学的数列问题,请详细说明一下,快一点,谢谢在数列（an)中,若a1+2a2+3a3+……nan=n(n+1)(n+2),则an=?答案是2n/n+1谢谢找到答案了a1+2a2+3a3+……+(n-1)a(n-1)=(n-1)n(n+1) 两式相减，nan＝3n(n+1) 于是an＝3n+3

由a(1)+2a(2)+3a(3)+……na(n)=n(n+1)(n+2)求出一些项观察一下:
a(1)=6=3(1+1)
a(2)=9=3(2+1)
a(3)=12=3(3+1)
a(4)=15=3(4+1)
所以,猜测
a(n)=3(n+1)
证明
当n=1时
a(1)=6=1*(1+1)*(1+2),正确
假设n=k时正确,即
a(1)+2a(2)+3a(3)+……ka(k)=k(k+1)(k+2)
当n=k+1时
a(1)+2a(2)+3a(3)+……ka(k)+(k+1)a(k+1)=
=k(k+1)(k+2)+(k+1)*3(k+1+1)=
=k(k+1)(k+2)+(k+1)*3(k+2)=
=(k+1)(k+2)(k+3)=
=(k+1)[(k+1)+1][(k+1)+2]
正确!