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HMMT 十一月 2013 · 团队赛 · 第 8 题

HMMT November 2013 — Team Round — Problem 8

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 2 ] Define the sequence { x } by x = x = x = 1 and x = for k > 2. Find x .
    i i ≥ 0 0 1 2 k 2013
    k − 3 x
解析

英文解析

  1. [ 2 ] Define the sequence { x } by x = x = x = 1 and x = for k > 2. Find x .
    i i ≥ 0 0 1 2 k 2013
    k − 3 x
    1+1+1 3+1+1 5+3+1 9+5+1
    Answer: 9 We have x = = 3, x = = 5, x = = 9, x = = 5. By
    3 4 5 6
    1 1 1 3
    the symmetry of our recurrence (or just further computation—it doesn’t matter much), x = 3 andx = x = x = 1, so our sequence has period 8. Thus x = x = x = 9.7
    8 9 10 2013 13 5