How would I use the Limit Comparison Test on this problem? <munderover> &#x2211;<!-- ∑ -->

raulgallerjv

raulgallerjv

Answered question

2022-05-19

How would I use the Limit Comparison Test on this problem?
n = 1 4 n + 5 n 4 n + 8 n

Answer & Explanation

exhumatql

exhumatql

Beginner2022-05-20Added 12 answers

As soon as you have obtained your first expression for the ratio, divide numerator and denominator by 5 n × 8 n
You will get with no trouble
1 + 4 n 5 n 1 + 4 n 8 n .
Now it is time to find the limit. I think that it is clear that
lim n 4 n 5 n = lim n 4 n 8 n = 0.
If we really want to give a proof of the above two facts, we can use L'Hospital's Rule, or other methods.

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