Name: College Algebra
Author: Blitzer
ISBN: 9780136970514

Ch. 8 - Sequences, Induction, and Probability

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Blitzer 8th Edition

Ch. 8 - Sequences, Induction, and Probability

Section 8.1

문제 1

Write the first four terms of each sequence whose general term is given. a_n=3n+2

문제 3

Write the first four terms of each sequence whose general term is given. a_n=3ⁿ

문제 5

Write the first four terms of each sequence whose general term is given. a_n=(−3)ⁿ

문제 7

Write the first four terms of each sequence whose general term is given. a_n=(−1)ⁿ(n+3)

문제 9

Write the first four terms of each sequence whose general term is given. a_n=2n/(n+4)

문제 11

In Exercises 1–12, write the first four terms of each sequence whose general term is given. a_n=(−1)ⁿ⁺¹/(2ⁿ−1)

문제 13

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=7 and a_n=a_n-1 + 5 for n≥2

문제 15

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=3 and a_n=4a_n-1 for n≥2

문제 17

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=4 and a_n=2a_n-1 + 3 for n≥2

문제 19

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n = n²/n!

문제 21

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n=2(n+1)!

문제 22

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n=−2(n−1)!

문제 23

Evaluate each factorial expression. 17!/15!

문제 24

Evaluate each factorial expression. 18!/16!

문제 25

Evaluate each factorial expression. 16!/2!14!

문제 27

Evaluate each factorial expression. (n+2)!/n!

문제 29

Find each indicated sum. $\sum_{i = 1}^{6} 5 i$

문제 31

Find each indicated sum. $\sum_{i = 1}^{4} 2 i^{2}$

문제 33

Find each indicated sum. $\sum_{k = 1}^{5} k (k + 4)$

문제 35

Find each indicated sum. $\sum_{i = 1}^{4} {(- \frac{1}{2})}^{i}$

문제 37

Find each indicated sum. $\sum_{i = 5}^{9} 11$

문제 39

Find each indicated sum. $\sum_{i = 0}^{4} \frac{(- 1)^{i}}{i!}$

문제 41

Find each indicated sum. $\sum_{i = 1}^{5} \frac{i!}{(i - 1)!}$

문제 43

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $1^{2} + 2^{2} + 3^{2} + \dots + 15^{2}$

문제 45

Express each sum using summation notation. Use $1$ as the lower limit of summation and $i$ for the index of summation. $2 + 2^{2} + 2^{3} + \dots + 2^{11}$

문제 47

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+2+3+⋯+ 30

문제 49

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1/2+2/3+3/4+⋯+ 14/(14+1)

문제 51

Express each sum using summation notation. Use $1$ as the lower limit of summation and $i$ for the index of summation. $4 + 4^{2} / 2 + 4^{3} / 3 + \dots + 4^{n} / n$

문제 53

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+3+5+⋯+ (2n−1)

문제 55

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. 5+7+9+11+⋯+ 31