Question
(A) Show that the series \(\sum_{n=1}^{\infty }\frac{n^{n}}{(3n)!}\) is convergent.
(B) Use part (a) to evaluate the limit \(\lim_{n\rightarrow \infty }\frac{n^{n}}{(3n)!}\).
Answer/Explanation
(A) Show that the series \(\sum_{n=1}^{\infty }\frac{n^{n}}{(3n)!}\) is convergent.
(B) Use part (a) to evaluate the limit \(\lim_{n\rightarrow \infty }\frac{n^{n}}{(3n)!}\).