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HMMT 十一月 2009 · GEN1 赛 · 第 10 题

HMMT November 2009 — GEN1 Round — Problem 10

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 8 ] Compute ( ) n n ( ) ( ) ∞ 3 3 ∏ 1 1 1 − + . 2 4 n =0
解析
  1. [ 8 ] Compute ( ) n n ( ) ( ) ∞ 3 3 ∏ 1 1 1 − + . 2 4 n =0 n +1 3 1 1+ ( ) 2 2 Answer: We can rewrite each term as . In the infinite product, each term of the form n 3 3 1 1+ ( ) 2 n ( ) 3 1 1 + with n > 0 appears once in the numerator and once in the denominator. The only remaining 2 ( ) 1 1 term is 1 + in the first denominator. 2