what is the lim((n+4)/(n+1))^n when it tend to infinity

help

you know that

lim (1 + 1/n)^n = e
In fact,
lim (1 + 1/(n+k))^n = e

(n+4)/(n+1) = 1 + 3/(n+1)

so, lim (1 + 3/(n+1)) = e^3

see whether you can justify that