One could show
lim n → ∞ a n = lim n → ∞ 2 n / 3 ( 2 + 7 / n ) 4 = ∞ {\displaystyle \lim _{n\to \infty }a_{n}=\lim _{n\to \infty }{\frac {2^{n/3}}{(2+7/n)^{4}}}=\infty }
directly, and thus conclude that the given series diverges from the Test for Divergence.