PUMaC 2015 · 加试 · 第 2 题
PUMaC 2015 — Power Round — Problem 2
题目详情
- It is not necessary to do the problems in order, although it is a good idea to read all the problems, so that you know what is permissible to assume when doing each problem. However, please collate the solutions in order in your solution packet. Each problem should start on a new page, and solutions should be written on one side of the paper only (there is a point deduction for not following this formatting).
解析
- This is true by induction. The base cases are easy. Then using the previous part a) above for the inductive step, note that 2 a s n − 1 2 n 2 s = 4 a ⇐⇒ = 4 a . n n n 2 a n − 1