Question

。。急求数学累加法

已知数列{an}中。A1=2，An+1=An+3n+2。求An. 注：An+1的角标为n+1急求详细解题过程

Answer 1

A（n+1）-An=3n+2S（n+1）-Sn=[A（n+1）-An]+[An-A(n-1)]+……+(A2-A1)+A1=2n+3*n*(1+n)/2+2=A(n+1)所以An=A（n+1）-3n-2，代入即可

Answer 2

∵An+1=An+3n+2∴An+1-An=3n+2∴A2-A1=3+2A3-A2=6+2A4-A3=9+2…………An-An-1=3(n-1)+2以上各式相加得到，A2-A1+A3-A2+A4-A3+……+An-An-1=3+9+……3(n-1)+2(n-1)∴An-A1=(3+3n-3)x(n-1)/2+2(n-1)∴An=(3n/2+2)(n-1)+2，n∈N*