We were given the hint to try using the Squeeze Theorem in order to find the limit of the sequence:
as n approaches ∞.
The expression can also be written as (taking the nth root of the expression).
I understand the concept of the squeeze theorem that I need to find functions greater and less than that limit to the same value so I can conclude that limits to that same value as well.
I don't know how to come up with those functions. It has been 2 years since I last took a calculus class, so I am very rusty with limits.
So far all I have is that 0 ≤ ≤ 2^n + 3^n.
So I can say 0 limits to 0, but then how would I evaluate
the limit of 2^n + 3^n as n approaches ∞? It would just keep getting bigger so I would have that limit as ∞. So I am stuck
Any help, tips, corrections, and/or suggestions is greatly appreciated.
Thank you for your time!