推 SoLs : 謝謝，已看懂 11/20 21:37
※ 引述《SoLs (SoLs)》之銘言：
: https://imgur.com/gallery/f4FeX
: 2.3.13
: 我已經證出有極限了
: 可是找不到極限值
: -----
: Sent from JPTT on my OPPO CPH1607.
0 < q < 1
[(1 - q) + q]/2 >= √[(1 - q)q]
=> (1 - q)q >= 1/4
(1 - q_n)q_(n+1) > 1/4 >= (1 - q_n)q_n
=> q_(n+1) > q_n
所以{q_n}嚴格遞增數列
因為有上界 => lim q_n 存在，設為a
n→∞
q_(n+1) > (1/4)/[1 - q_n] > q_n
=> a = (1/4)/[1 - a]
=> 4a - 4a^2 = 1
=> a = 1/2 = lim q_n
n→∞
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