Q. 251 In the following exercises, usin... [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 11: Q. 251 (page 1069)

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

Short Answer

Expert verified

The first five terms of the sequence are $\frac{1}{6}, \frac{1}{12}, \frac{1}{20}, \frac{1}{30},$ and $\frac{1}{42}$ .

Step by step solution

Step 1. Given information.

The given general term is,

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

Step 2. Finding the first five terms.

Now, to find the first five terms of the sequence we will substitute $1, 2, 3, 4,$ and $5$ respectively in the general term then we get,

$a_{n} = \frac{n!}{(n + 2)!}$	$a_{n} = \frac{n!}{(n + 2)!}$	$a_{n} = \frac{n!}{(n + 2)!}$	$a_{n} = \frac{n!}{(n + 2)!}$	$a_{n} = \frac{n!}{(n + 2)!}$
$a_{1} = \frac{1}{(3)!}$	$a_{2} = \frac{2!}{(4)!}$	$a_{3} = \frac{3!}{(5)!}$	$a_{4} = \frac{4!}{(6)!}$	$a_{5} = \frac{5!}{(7)!}$
$a_{1} = \frac{1}{3.2.1}$	localid="1668005252784" role="math" $a_{2} = \frac{2 路 1}{4 路 3 路 2 路 1}$	localid="1668005262205" role="math" $a_{3} = \frac{3 路 2 路 1}{5 路 4 路 3 路 2 路 1}$	localid="1668005273995" role="math" $a_{4} = \frac{4 路 3 路 2 路 1}{6 路 5 路 4 路 3 路 2 路 1}$	localid="1668005246335" role="math" $a_{5} = \frac{5 路 4 路 3 路 2 路 1}{7 路 6 路 5 路 4 路 3 路 2 路 1}$
$a_{1} = \frac{1}{6}$	$a_{2} = \frac{1}{12}$	$a_{3} = \frac{1}{20}$	$a_{4} = \frac{1}{30}$	$a_{5} = \frac{1}{42}$

Therefore, the first five terms of the sequence are localid="1645342057494" $\frac{1}{6}, \frac{1}{12}, \frac{1}{20}, \frac{1}{30},$ and $\frac{1}{42}$ .

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91影视

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding the first five terms.

One App. One Place for Learning.

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91影视

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.an=n!n+2!

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding the first five terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Calculus

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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