Question

write the first four terms of the sequence whose general term is given below.
$a_n = \frac{n^4}{n!}$
$a_1 = \square$
(type an integer or a simplified fraction.)

Explanation:

Step1: Substitute n = 1 into the formula

To find \( a_1 \), we substitute \( n = 1 \) into the general term \( a_n=\frac{n^4}{n!} \).
First, calculate \( n^4 \) when \( n = 1 \): \( 1^4 = 1 \).
Then, calculate \( n! \) when \( n = 1 \): \( 1! = 1 \).
So, \( a_1=\frac{1^4}{1!}=\frac{1}{1} \).

Step2: Simplify the fraction

\( \frac{1}{1}=1 \).

Answer:

1