Is {a_n} Bounded Above by 3 in Calculus?

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The discussion focuses on proving that the sequence {a_n} is increasing and bounded above by 3. Being bounded above by 3 means that all terms of the sequence are less than or equal to 3. This concept is crucial in calculus for understanding the behavior and limits of sequences. To demonstrate this property, induction or alternative methods can be employed to show that each term in the sequence adheres to this upper limit. Establishing that {a_n} does not exceed 3 is essential for analyzing its convergence and overall characteristics.
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This is in Calculus about sequences.

Question...

By induction or otherwise, show that {a_n} is increasing and bounded above by 3.

What do they mean by bounded above by 3?
 
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They mean simply that the terms of the sequence must be \leq 3. It is an upper bound for the sequence.
 
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In this context, bounded above by 3 means that the sequence {a_n} will never exceed the value of 3. In other words, the terms in the sequence will always be less than or equal to 3. This is an important concept in calculus, as it helps to determine the behavior and limits of a sequence. In order to show that {a_n} is bounded above by 3, you will need to use induction or another method to prove that each term in the sequence is less than or equal to 3.
 

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