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HMMT 二月 2009 · 代数 · 第 2 题

HMMT February 2009 — Algebra — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

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