HMMT 二月 2012 · 冲刺赛 · 第 2 题
HMMT February 2012 — Guts Round — Problem 2
题目详情
英文原题
[2] Let a0, a1, a2, . . . denote the sequence of real numbers such that a0= 2 and an+1=an 1+anforn≥0. Compute a2012.
解析
英文解析
- [ 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+ an
Compute a .
2012
2 2
Answer: Calculating out the first few terms, note that they follow the pattern a = .
4025 2 n +1 n
Plugging this back into the recursion shows that it indeed works.