HMMT 二月 2012 · 冲刺赛 · 第 2 题
HMMT February 2012 — Guts Round — Problem 2
题目详情
- [ 2 ] Let a , a , a , . . . denote the sequence of real numbers such that a = 2 and a = for n ≥ 0. 0 1 2 0 n +1 1+ a n Compute a . 2012
解析
- [ 2 ] Let a , a , a , . . . denote the sequence of real numbers such that a = 2 and a = for n ≥ 0. 0 1 2 0 n +1 1+ a n Compute a . 2012 2 2 Answer: Calculating out the first few terms, note that they follow the pattern a = . n 4025 2 n +1 Plugging this back into the recursion shows that it indeed works.