已知数列an满足a1+2a2+3a3+……+nan=n(n+1)(n+2),则它的前n项和Sn=?（9n+3n²）/2）
问题描述：
已知数列an满足a1+2a2+3a3+……+nan=n(n+1)(n+2),则它的前n项和Sn=?
（9n+3n²）/2）
答
an =[ n(n+1)(n+2) - (n-1)n(n+1) ] / n = 3(n+1)
则前n项和是 (a1 + an)*n/2 = (6 + 3n+3)n/2 = (3n^2+9n)/2
答
设a1+2a2+3a3+……+nan=Tn
则Tn=n(n+1)(n+2)
T(n-1)=n(n-1)(n+1)
nan=Tn-T(n-1)=3n(n+1)
an=3(n+1)
Sn=3(1+1)+3(2+1)+...+3(n+1)
=3n(n+3)/2=(3n^2+9n)/2