1．数列（an)中,a1=1,a(n+1)=an+2n,求an

题目

1．数列（an)中,a1=1,a(n+1)=an+2n,求an
2.,a1=3,a(n+1)=an*2^n,求an
*上面的a1中的"1"是角标,后面的"n+1","n",都是角标...

答案

1、叠加an=a1+k=1到n-1∑2k=n^2-n+1
2、叠乘
an=a1*(a2/a1)*(a3/a2)*……*(an/an-1)=3*2*2^2*……*2^(n-1)
=3*2^[n(n-1)/2]