Q. 12.16 Write the first five terms of th... [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. 12.16 (page 1169)

Write the first five terms of the sequence whose general term is $a_{n} = \frac{n!}{(n + 1)!}$ .

Short Answer

Expert verified

The first five terms of the sequence with general term $a_{n} = \frac{n!}{(n + 1)!}$ are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5} and \frac{1}{6} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegeneraltermisgivenas \\ a_{n} = \frac{n!}{(n + 1)!} \\ Wehavetowritethefirst5termsofthesequence. \end{array}$

Step 2. Calculating the first five terms

We substitute the values 1, 2, 3, 4, 5 into the formula for the general term.

$\begin{array}{l} Weknow \\ If n isapositiveinteger,then \\ 鈬� n! = n (n 鈭� 1) (n 鈭� 2) 鈥� \end{array}$

Now,

$\begin{matrix} n = 1 & n = 2 & n = 3 & n = 4 & n = 5 \\ \begin{array}{l} 鈬� a_{1} = \frac{1!}{(1 + 1)!} \\ = \frac{1!}{2!} \\ = \frac{1}{2 脳 1} \\ = \frac{1}{2} \end{array} & \begin{array}{l} 鈬� a_{2} = \frac{2!}{(2 + 1)!} \\ = \frac{2 脳 1!}{3!} \\ = \frac{2}{3 脳 2 脳 1} \\ = \frac{1}{3} \end{array} & \begin{array}{l} 鈬� a_{3} = \frac{3!}{(3 + 1)!} \\ = \frac{3!}{4!} \\ = \frac{3 脳 2 脳 1}{4 脳 3 脳 2 脳 1} \\ = \frac{1}{4} \end{array} & \begin{array}{l} 鈬� a_{4} = \frac{4!}{(4 + 1)!} \\ = \frac{4!}{5!} \\ = \frac{4 脳 3 脳 2 脳 1}{5 脳 4 脳 3 脳 2 脳 1} \\ = \frac{1}{5} \end{array} & \begin{array}{l} 鈬� a_{5} = \frac{5!}{(5 + 1)!} \\ = \frac{5!}{6!} \\ = \frac{5 脳 4 脳 3 脳 2 脳 1}{6 脳 5 脳 4 脳 3 脳 2 脳 1} \\ = \frac{1}{6} \end{array} \end{matrix}$

Step 3. Conclusion

From the above step, we can observe that the first five terms of the sequence will be $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5} and \frac{1}{6} .$

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91影视

Write the first five terms of the sequence whose general term is $a_{n} = \frac{n!}{(n + 1)!}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the first five terms

Step 3. Conclusion

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91影视

Write the first five terms of the sequence whose general term is an=n!(n+1)!.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the first five terms

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Applied Mathematics

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Write the first five terms of the sequence whose general term is $a_{n} = \frac{n!}{(n + 1)!}$ .