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HMMT 二月 2008 · 冲刺赛 · 第 11 题

HMMT February 2008 — Guts Round — Problem 11

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 7 ] Let f ( r ) = = + + · · · + . Find f ( k ). r r r r j =2 k =2 j 2 3 2008
解析
  1. [ 7 ] Let f ( r ) = = + + · · · + . Find f ( k ). r r r r j =2 k =2 j 2 3 2008 2007 Answer: We change the order of summation: 2008 ( ) ∞ 2008 2008 ∞ 2008 2008 2008 ∑ ∑ ∑ ∑ ∑ ∑ ∑ 1 1 1 1 1 1 1 2007 = = = = − = 1 − = . 1 k k 2 j j j (1 − ) j ( j − 1) j − 1 j 2008 2008 j j =2 j =2 j =2 j =2 j =2 k =2 k =2