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Chapter 8: Problem 19

The general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. $$a_{n}=\frac{n^{2}}{n !}$$

Short Answer

Expert verified
The first four terms of the sequence are 1, 2, 3, and 2.

Step by step solution

01

Substitute n=1 into the general term

First, \(n=1\) is substituted into the equation to get the first term: \(a_{1}=\frac{1^{2}}{1 !} = 1\)
02

Substitute n=2 into the general term

Next, \(n=2\) is substituted into the equation to generate the second term: \(a_{2}=\frac{2^{2}}{2 !} = 2\)
03

Substitute n=3 into the general term

Thirdly, \(n=3\) is substituted into the equation to generate the third term: \(a_{3}=\frac{3^{2}}{3 !} = 3\)
04

Substitute n=4 into the general term

Finally, \(n=4\) is substituted into the equation to generate the fourth term: \(a_{4}=\frac{4^{2}}{4 !} = 2\)

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