Q. 43 In the following exercise, using... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 43 (page 1174)

In the following exercise, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{(n 鈭� 1)!}{(n)!}$

Short Answer

Expert verified

The first five terms of the sequence whose general term is $a_{n} = \frac{(n 鈭� 1)!}{(n)!}$ are $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ .

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegeneraltermsforthesequenceisgivenas \\ a_{n} = \frac{(n 鈭� 1)!}{(n)!} \\ Wehavetofindthefirstfivetermsforthesequence. \end{array}$

Step 2. Calculating the terms

$\begin{array}{l} Now, \\ Weknow, \\ 鈬� n! = n (n 鈭� 1) (n 鈭� 2) (n 鈭� 3) ... \end{array}$

localid="1645627181343" $\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 \\ a_{n} : & \begin{array}{l} a_{1} = \frac{(1 鈭� 1)!}{(1)!} \\ = \frac{0!}{1!} \\ = \frac{1}{1} \\ = 1 \end{array} & \begin{array}{l} a_{2} = \frac{(2 鈭� 1)!}{(2)!} \\ = \frac{1!}{2!} \\ = \frac{1}{2 脳 1} \\ = \frac{1}{2} \end{array} & \begin{array}{l} a_{3} = \frac{(3 鈭� 1)!}{(3)!} \\ = \frac{2!}{3!} \\ = \frac{2 脳 1}{3 脳 2 脳 1} \\ = \frac{1}{3} \end{array} & \begin{array}{l} a_{2} = \frac{(4 鈭� 1)!}{(4)!} \\ = \frac{3!}{4!} \\ = \frac{3 脳 2 脳 1}{4 脳 3 脳 2 脳 1} \\ = \frac{1}{4} \end{array} & \begin{array}{l} a_{2} = \frac{(5 鈭� 1)!}{(5)!} \\ = \frac{4!}{5!} \\ = \frac{4 脳 3 脳 2 脳 1}{5 脳 4 脳 3 脳 2 脳 1} \\ = \frac{1}{5} \end{array} \end{matrix}$

Step 3. Conclusion

From the above table, we can observe that the first five terms of sequence will be $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5} .$

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91影视

In the following exercise, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{(n 鈭� 1)!}{(n)!}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

Step 3. Conclusion

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91影视

In the following exercise, using factorial notation, write the first five terms of the sequence whose general term is given. an=n鈭�1!n!

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the terms

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

In the following exercise, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{(n 鈭� 1)!}{(n)!}$