Re: [中學] 比大小

[keith291 (keith)]

※ 引述《opagainop (12345)》之銘言：
: A = (1/2)(3/4)(5/6)(7/8)........(99/100)
: B = (2/3)(4/5)(6/7)(8/9)........(100/101)
: C = 1/10
: D = 1/11
: 試求 A,C (比大小)
:      B,D (比大小)
: 感謝各位高手解題  ^^

首先,因為1/2 < 2/3 , 3/4 < 4/5 ....99/100 < 100/101

顯然 A < B

故 A^2 < AB = 1/101 → A < 1/√101 < 1/√100 = 1/10 = C

且 1/101 = AB < B^2 → B > 1/√101 > 1/√121 = 1/11 = D

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推 opagainop   : 感謝