盒子里放有三只小球,魔术师第一次从盒子里拿出一只小球,将它变成3只小球后放回盒子里

2025-05-11 11:19:44
推荐回答(1个)
回答1:

答案113.

设第n次有a_n个球. 则有递推关系
a_n=a_{n-1}-n+3n=a_{n-1}+2n.
故a_n
=a_{n-1}+2n
=a_{n-2}+2(n-1)+2n
=a_{n-3}+2(n-2)+2(n-1)+2n
=...
=a_0+2*(1+2+3+...+n)
=3+n(n+1)
=n^2+n+3.
故a_{10}=113.