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If is a real number greater than 1 , which of the following must be true for the value of ?

Ask by Curry Griffin. in the United States
Jan 23,2025

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If is a real number greater than 1, then must be less than 1.

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Bonus Knowledge

Since is a real number greater than 1, we know that is the reciprocal of . Therefore, as increases, also increases, making decrease. Specifically, since , it follows that , and consequently, . Thus, must always be a positive number that is less than 1.
In practical terms, using values can illustrate this. For instance, if , then , which is indeed less than 1. The more significant implication here is that will always be a positive fraction for any real , reinforcing that it approaches zero but never actually reaches it as grows larger.

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