HMMT 二月 2007 · 代数 · 第 1 题

HMMT February 2007 — Algebra — Problem 1

专题: Discrete Math / 离散数学
难度: L3
来源: HMMT

题目详情

[ 3 ] Compute ⌊ ⌋ 2007! + 2004! . 2006! + 2005! (Note that b x c denotes the greatest integer less than or equal to x .) 3 3

解析

[ 3 ] Compute ⌊ ⌋ 2007! + 2004! . 2006! + 2005! (Note that b x c denotes the greatest integer less than or equal to x .) Answer: 2006 . We have ⌊ ( ⌋ ) ⌊ ⌋ ⌊ ⌋ ⌊ ⌋ 1 1 2007 · 2006 + · 2005! 2007 · 2006 + 2007! + 2004! 1 2005 2005 = = = 2006 + . 2006! + 2005! (2006 + 1) · 2005! 2007 2005 · 2007 3 3