Question
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
Upstudy AI Solution
Tutor-Verified Answer
Answer
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.