若数列{An}中,A1=3,An+1=An+n²/3,则数列{An}的通项An=?

题目

若数列{An}中,A1=3,An+1=An+n²/3,则数列{An}的通项An=?

答案

1²+2²+3²+……=n(n+1)(2n+1)/6
a2=a1+1²/3
:
an=an-1+（n-1)²/3
累加得
an=a1+1²/3+2²/3+……(n-1)²/3
an=3+(n-1)n(2n-1)/18