Use the Growth Rates of Sequences Theorem to find the limit of the following sequence or state that it diverges. \( \left\{\frac{4^{5 n}}{n!}\right\} \) Select the correct choice below and fill in any answer boxes within your choice. A. The limit of the sequence is B. The sequence diverges.

To find the limit of the sequence \( \left\{\frac{4^{5n}}{n!}\right\} \), we can use the Growth Rates of Sequences Theorem. As \( n \) approaches infinity, we note that \( n! \) grows much faster than \( 4^{5n} \). In fact, while \( 4^{5n} \) represents exponential growth, \( n! \) reflects factorial growth, which outpaces exponential functions. Therefore, A. The limit of the sequence is \( 0 \).