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HMMT 二月 2013 · 冲刺赛 · 第 13 题

HMMT February 2013 — Guts Round — Problem 13

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 8 ] Find the smallest positive integer n such that > 4 . 99.
    n n
    5 +2
解析

英文解析

  1. [ 8 ] Find the smallest positive integer n such that > 4 . 99.
    n n
    5 +2
    n +1 n n +1 n n n
    Answer: 7 Writing 5 = 5 · 5 and 2 = 2 · 2 and cross-multiplying yields 0 . 01 · 5 > 2 . 99 · 2 ,
    and re-arranging yields (2 . 5) > 299. A straightforward calculation shows that the smallest n for whichnthis is true is n = 7.