I can think of a number of ways

abitinomaq1

abitinomaq1

Answered question

2022-03-30

I can think of a number of ways to prove that limn(4nn4)=

Answer & Explanation

Pubephenedsjq

Pubephenedsjq

Beginner2022-03-31Added 11 answers

The second term is very small compared to the first as n gets large. Specifically
limn4nn44n=limn(1n44n)
=1limnn44n
The limit on the right can be shown to be zero in several ways, such as applying L'hopital's rule several times. So the ratio goes to 1 as n goes to infinity. As a result,
limn4nn4=limn{4nn4over4n}4n
=limn{4nn44n}limn4n
=
Alternatively, the above limit shows that for n large enough you have
{4nn44n}>12
So since limn4n=,limn4nn4= as well

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