[中學] 絕對値不等式
各位前輩好，有個絕對値不等式的地方卡住了，希望前輩們能指點一下：
m, n, s, t 均為正整數。
m log t m 1
--- ≦ ------- ≦ --- + --- (1)
n log s n n
所以
| m log t | 1
| --- - ------- | < --- (2)
| n log s | n
不清楚為何(1)可以變成(2)？
用畫圖的方式雖然可以了解，但是如果從(2)回推到(1)：
-1 m log t 1
--- < --- - ------- < ---
n n log s n
-1-m -log t 1-m
----- < ------- < -----
n log s n
m-1 log t m + 1
----- < ------- < -------
n log s n
和(1)的左項少了一個-1，請問是我哪裡寫錯了呢？
m log t m 1
--- ≦ ------- ≦ --- + --- (1)
n log s n n
感謝前輩們的指導。
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