Q. 252 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 12: Q. 252 (page 1217)

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

Short Answer

Expert verified

The first five terms of the sequence are $\frac{1}{4}, \frac{1}{9}, \frac{1}{8}, \frac{6}{25},$ and $\frac{2}{3}$ .

Step by step solution

Step 1. Given information.

The given general term is,

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

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,

$a_{n} = \frac{(n - 1)!}{{(n + 1)}^{2}}$	$a_{n} = \frac{(n - 1)!}{{(n + 1)}^{2}}$	$a_{n} = \frac{(n - 1)!}{{(n + 1)}^{2}}$	$a_{n} = \frac{(n - 1)!}{{(n + 1)}^{2}}$	$a_{n} = \frac{(n - 1)!}{{(n + 1)}^{2}}$
$a_{1} = \frac{(1 - 1)!}{{(1 + 1)}^{2}}$	$a_{2} = \frac{(2 - 1)!}{{(2 + 1)}^{2}}$	$a_{3} = \frac{(3 - 1)!}{{(3 + 1)}^{2}}$	$a_{4} = \frac{(4 - 1)!}{{(4 + 1)}^{2}}$	$a_{5} = \frac{(5 - 1)!}{{(5 + 1)}^{2}}$
$a_{1} = \frac{1}{{(2)}^{2}}$	$a_{2} = \frac{1}{{(3)}^{2}}$	$a_{3} = \frac{2.1}{4.4}$	$a_{4} = \frac{3.2.1}{5.5}$	$a_{5} = \frac{4.3.2.1}{6.6}$
$a_{1} = \frac{1}{4}$	$a_{2} = \frac{1}{9}$	$a_{3} = \frac{1}{8}$	role="math" localid="1645347914333" $a_{4} = \frac{6}{25}$	$a_{5} = \frac{2}{3}$

Therefore, the first five terms of the sequence are $\frac{1}{4}, \frac{1}{9}, \frac{1}{8}, \frac{6}{25},$ and $\frac{2}{3}$ .

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding the first five terms.

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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-1!n+12

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

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