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HMMT 二月 2001 · ADV 赛 · 第 3 题

HMMT February 2001 — ADV Round — Problem 3

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. Calculate the sum of the coefficients of P ( x ) if (20 x + 2 x + 1) P ( x ) = 2001 x .
解析

英文解析

  1. Calculate the sum of the coefficients of P ( x ) if (20 x + 2 x + 1) P ( x ) = 2001 x .
    Solution: The sum of coefficients of f ( x ) is the value of f (1) for any polynomial f .
    2001
    Plugging in 1 to the above equation, P (1) = = 87 .
    23