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Gybrisysmemiau7 2022-06-07 Answered
How do I prove that:
lim n 4 n + 9 n 2 n = 4
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Answers (1)

Raven Higgins
Answered 2022-06-08 Author has 17 answers
Squeeze theorem:
For n 4
and so
4 4 n + 9 n 2 n 2 1 / n × 4
(We used 9 n 2 < 4 n for n 4, which has an easy proof using induction).
Since 2 1 / n 1 as n , the result follows.
To prove that 2 1 / n 1 one way to see this is to use the following standard theorem:
If a n > 0 and lim n a n + 1 a n = L, then lim n a n 1 / n = L. You pick a n = 2. Of course, you could use this theorem on your original sequence itself...
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