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GRE數學: 比較大小 t is an integer

Aug 12th 2014, 07:56

陳向東：快速數學突破 P. 78 第28題

t is an integer

Compare

A) 1/(1+2^t)
B) 1/(1+3^t)

Answer: 無法比較
解釋：比較二者大小，實際是比較2^t和3^t大小，而 2^t 和 3^t 大小又依賴于 t 的取值

t > 0時，2^t < 3^t
t = 0時，2^t = 3^t
t < 0時，2^t > 3^t

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我可以理解單純只用2^t 和 3^t 來做比較

但是回到原來 (A) 和 (B) 的式子時，將 t 代入 -1, 0 或 1
怎麼算都是 1/ (1+2^t) 比較大？! ！
覺得非常的奇怪呢！請問有人可以解答是哪裡的思路有問題呢？
謝謝

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