lim n→∞ [(n+1)^4/5^(n+1)]/[n^4/5^n] Why is it equal to 1 / 5,

lim n→∞ [(n+1)^4/5^(n+1)]/[n^4/5^n] Why is it equal to 1 / 5,

Original formula = Lim n →∞ ((n + 1) / N) ^ 4 / 5
lim n→∞((n+1)/n)=1
So the original formula is 1 / 5

LIM (n →∞) (1 + 1 / N) ^ n = e, find LIM (n →∞) (1 + 1 / N) ^ 5 + n

It should be LIM (n →∞) (1 + 1 / N) ^ (5 + n), right?
In this case, it should still be e,
Original formula = Lim [(1 + 1 / N) ^ n] * [(1 + 1 / N) ^ 5],
When n →∞, Lim [(1 + 1 / N) ^ n and lim (1 + 1 / N) ^ 5] exist, so they can be separated
=lim[(1+1/n)^n]*[lim(1+1/n)^5]=e*1=e