Is {a_n} Bounded Above by 3 in Calculus?

[JasonRox]

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?

 

[cepheid]

They mean simply that the terms of the sequence must be $\leq 3$. It is an upper bound for the sequence.

 

[thepatientmental]

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.