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HMMT 二月 2009 · 代数 · 第 2 题

HMMT February 2009 — Algebra — Problem 2

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 3 ] Let S be the sum of all the real coefficients of the expansion of (1 + ix ) . What is log ( S )? 2
解析

英文解析

  1. [ 3 ] Let S be the sum of all the real coefficients of the expansion of (1 + ix ) . What is log ( S )?
    Answer: 10042
    2009
    Solution: The sum of all the coefficients is (1 + i ) , and the sum of the real coefficients is the real
    ( )
    2009 2009
    10041
    part of this, which is (1 + i ) + (1 − i ) = 2 . Thus log ( S ) = 1004.
    22