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HMMT 十一月 2009 · GEN1 赛 · 第 10 题

HMMT November 2009 — GEN1 Round — Problem 10

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 8 ] Compute
    ( )
    n n
    ( ) ( )
    ∞
    3 3
    ∏
    1 1
    1 − + .
    2 4
    n =0
解析

英文解析

  1. [ 8 ] Compute
    ( )
    n n
    ( ) ( )
    ∞
    3 3
    ∏
    1 1
    1 − + .
    2 4
    n =0
    n +1
    1+13
    ( )
    2 2
    Answer: We can rewrite each term as . In the infinite product, each term of the formn
    3 13
    1+
    ( )
    n 2
    ( )
    1 + with n > 0 appears once in the numerator and once in the denominator. The only remaining 13
    ( )2
    term is 1 + in the first denominator.11 2