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HMMT 十一月 2017 · 冲刺赛 · 第 5 题

HMMT November 2017 — Guts Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 3 ] Define a sequence { a } by a = 1 and a = ( a )! + 1 for every n > 1. Find the least n for which n 1 n n − 1 10 a > 10 . n
解析
  1. [ 3 ] Define a sequence { a } by a = 1 and a = ( a )! + 1 for every n > 1. Find the least n for which n 1 n n − 1 10 a > 10 . n Proposed by: Michael Tang Answer: 6 We have a = 2, a = 3, a = 7, a = 7! + 1 = 5041, and a = 5041! + 1. But 2 3 4 5 6 10 5041! + 1 5041 · 5040 · 5039 > 10 . Hence, the answer is 6 .