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👨🏻‍🏫 學術台數學

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2010-03-06 2:15 am

證明

(1/2)x(3/4)x(5/6)x......x(2023/2024)<1/45

回答 (4)

用戶2053

2010-03-06 4:53 am

✔ 最佳答案

因 :
(1/2) x (3/4) x (5/6) x......x (2023/2024) < (2/3) x (4/5) x (6/7) x...x (2024/2025)

(1/2) x (3/4) x (5/6) x......x (2023/2024)
< (2/1) x (4/3) x (6/5) x (8/6) x ...... x (2024/2023) / 2025

令 (1/2) x (3/4) x (5/6) x......x (2023/2024) = N ,
N < (1/N) / 2025
N^2 < 1 / 2025
N < 1/45

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