Q. 47 In the following exercise, using... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 47 (page 1174)

In the following exercise, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{(n + 1)!}{n^{2}}$

Short Answer

Expert verified

The first five terms of the sequence whose general term is $a_{n} = \frac{(n + 1)!}{n^{2}}$ are $2, \frac{3}{2}, \frac{8}{3}, \frac{15}{2}, \frac{144}{5} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegeneraltermsforthesequenceisgivenas \\ a_{n} = \frac{(n + 1)!}{n^{2}} \\ Wehavetofindthefirstfivetermsforthesequence. \end{array}$

Step 2. Calculating the terms

$\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 \\ a_{n} : & \begin{array}{l} a_{1} = \frac{(1 + 1)!}{1^{2}} \\ = \frac{2!}{1} \\ = 2 \end{array} & \begin{array}{l} a_{2} = \frac{(2 + 1)!}{2^{2}} \\ = \frac{3!}{4} \\ = \frac{3 脳 2 脳 1}{4} \\ = \frac{3}{2} \end{array} & \begin{array}{l} a_{3} = \frac{(3 + 1)!}{3^{2}} \\ = \frac{4!}{9} \\ = \frac{4 脳 3 脳 2 脳 1}{9} \\ = \frac{8}{3} \end{array} & \begin{array}{l} a_{4} = \frac{(4 + 1)!}{4^{2}} \\ = \frac{5!}{16} \\ = \frac{5 脳 4 脳 3 脳 2 脳 1}{4} \\ = \frac{15}{2} \end{array} & \begin{array}{l} a_{5} = \frac{(5 + 1)!}{5^{2}} \\ = \frac{6!}{25} \\ = \frac{6 脳 5 脳 4 脳 3 脳 2 脳 1}{4} \\ = \frac{144}{5} \end{array} \end{matrix}$

Step 3. Conclusion

From the above table, we can observe that the first five terms of sequence will be $2, \frac{3}{2}, \frac{8}{3}, \frac{15}{2}, \frac{144}{5} .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In the following exercise, using factorial notation, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{(n + 1)!}{n^{2}}$

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

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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+1!n2

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

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Statistics

Applied Mathematics

Mechanics Maths

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.
$a_{n} = \frac{(n + 1)!}{n^{2}}$