Stewart – Calculus ET 8e Chapter 11 Form A
1. Find a formula for the general term of the sequence, assuming that the pattern of the first few
terms continues.
2. Find the partial sum of the series . Give your answer to five decimal places.
3. How many terms of the series would you need to add to find its sum to within
0.02?
4. Test the series for convergence or divergence.
5. Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.
6. Test the series for convergence or divergence.
7. Test the series for convergence or divergence.
8. Use the binomial series to expand the function as a power series. Find the radius of convergence.
Stewart – Calculus ET 8e Chapter 11 Form A
9. Find the sum of the series.
10. Use the Alternating Series Estimation Theorem or Taylor’s Inequality to estimate the range of
values of x for which the given approximation is accurate to within the stated error.
Write a such that .
11. Write the first five terms of the sequence whose term is given.
12. Find an expression for the term of the sequence. (Assume that the pattern continues.)
13. Determine whether the given series converges or diverges. If it converges, find its sum.
14. Determine whether the given series is convergent or divergent.
15. Determine whether the series converges or diverges.
Stewart – Calculus ET 8e Chapter 11 Form A
16. Test the series for convergence or divergence.
17. Determine whether the series converges or diverges.
18. Determine whether the series is convergent or divergent.
19. Determine whether the series is convergent or divergent.
20. Determine whether the series is convergent or divergent.
Stewart – Calculus ET 8e Chapter 11 Form A
Answer Key
Stewart – Calculus ET 8e Chapter 11 Form B
1. Determine whether the sequence converges or diverges. If it converges, find the limit.
2. Find the exact value of the limit of the sequence defined by .
3. The terms of a series are defined recursively by the equations .
Determine whether converges or diverges.
4. Express the number
as a ratio of integers.
5. Use the Integral Test to determine whether the series is convergent or divergent.
6. How many terms of the series would you need to add to find its sum to within
0.02?
7. Test the series for convergence or divergence.
8. Determine whether the sequence convergent or divergent.
9. Test the series for convergence or divergence.
Stewart – Calculus ET 8e Chapter 11 Form B
10. Test the series for convergence or divergence.
11. Find a power series representation for the function and determine the radius of convergence.
12. Find the Maclaurin series for using the definition of a Maclaurin serires.
13. Use the binomial series to expand the function as a power series. Find the radius of convergence.
14. Use the Alternating Series Estimation Theorem or Taylor’s Inequality to estimate the range of
values of x for which the given approximation is accurate to within the stated error.
Write a such that .
15. Use the sum of the first 9 terms to approximate the sum of the following series.
Write your answer to six decimal places.
16. Determine whether the series is convergent or divergent.
Stewart – Calculus ET 8e Chapter 11 Form B
17. Determine whether the series converges or diverges.
18. Determine whether the series is convergent or divergent.
19. Determine whether the series is convergent or divergent.
20. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
Stewart – Calculus ET 8e Chapter 11 Form B
Answer Key
Stewart – Calculus ET 8e Chapter 11 Form C
Select the correct answer for each question.
____ 1. Determine whether the sequence defined by converges or diverges. If it converges,
find its limit.
a.
b. –5
c.
d. Diverges
____ 2. Determine whether the sequence defined by converges or diverges. If it converges,
find its limit.
a. 1
b.
c. 0
d. Diverges
____ 3. Find the value of the limit for the sequence given.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 11 Form C
____ 4. If $600 is invested at interest, compounded annually, then after n years the investment is
worth dollars. Find the size of investment after 7 years.
a. $430.21
b. $1,860.81
c. $1,230.81
d. $789.56
e. $1,321.06
____ 5. Determine whether the geometric series converges or diverges. If it converges, find its sum.
a. 30
b. 36
c. 5
d. Diverges
____ 6. A sequenceis defined recursively by the equation for where
.
Use your calculator to guess the limit of the sequence.
a.
b. 14
c.
d.
e. 15
Stewart – Calculus ET 8e Chapter 11 Form C
____ 7. Determine whether the geometric series converges or diverges. If it converges, find its sum.
a.
b.
c. Diverges
d.
____ 8. Find all positive values of u for which the series converges.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 11 Form C
____ 9. Determine which one of the p-series below is divergent.
a.
b.
c.
d.
____ 10. Find an approximation of the sum of the series accurate to two decimal places.
a. –1.06
b. –0.84
c. –0.90
d. –0.98
____ 11. Approximate the sum to the indicated accuracy.
(five decimal places)
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 11 Form C
____ 12. Find the radius of convergence and the interval of convergence of the power series.
a.
b.
c.
d.
____ 13. Find the radius of convergence and the interval of convergence of the power series.
a.
b.
c.
d.
____ 14. Find the interval of convergence of the series.
a.
b.
c.
d. diverges everywhere
e.
Stewart – Calculus ET 8e Chapter 11 Form C
____ 15. Find a power series representation for
a.
b.
c.
d.
e.
____ 16. Use the power series for to estimate correct to four decimal places.
a.
b.
c.
d.
e.
____ 17. Use series to approximate the definite integral to within the indicated accuracy.
a. 0.0354
b. 0.0125
c. 0.0625
d. 0.1447
e. 0.2774
Stewart – Calculus ET 8e Chapter 11 Form C
____ 18. Use series to evaluate the limit correct to three decimal places.
Select the correct answer.
a. 118.933
b. 114.133
c. 34.3233
d. 114.333
e. 115.933
____ 19. For which positive integers k is the series convergent?
a.
b.
c.
d.
e.
____ 20. Which of the given series are absolutely convergent?
a.
b.
Stewart – Calculus ET 8e Chapter 11 Form C
Answer Key
Stewart – Calculus ET 8e Chapter 11 Form D
Select the correct answer for each question.
____ 1. Find the value of the limit for the sequence given.
a.
b.
c.
d.
e.
____ 2. Determine whether the sequence defined by converges or diverges. If it
converges, find its limit.
a. 13
b. 5
c. Diverges
d. –3
____ 3. Determine whether the geometric series converges or diverges. If it converges, find its sum.
a. 12
b. Diverges
c. 3
d. 16
____ 4. Determine whether the geometric series converges or diverges. If it converges, find its sum.
a. 30
b. 36
c. 5
d. Diverges
Stewart – Calculus ET 8e Chapter 11 Form D
____ 5. A rubber ball is dropped from a height of 8 m onto a flat surface. Each time the ball hits the
surface, it rebounds to 50% of its previous height. Find the total distance the ball travels.
a. 16
b. 24
c. 8
d. 32
____ 6. A sequenceis defined recursively by the equation for where
.
Use your calculator to guess the limit of the sequence.
a.
b. 14
c.
d.
e. 15
____ 7. Find the sum of the series.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 11 Form D
____ 8. Find all positive values of u for which the series converges.
a.
b.
c.
d.
e.
____ 9. Find all values of p for which the series converges.
a.
b.
c.
d.
____ 10. Determine whether the sequence convergent or divergent.
a. converges
b. diverges
____ 11. Test the series for convergence or divergence.
a. The series is convergent.
b. The series is divergent.
Stewart – Calculus ET 8e Chapter 11 Form D
____ 12. Determine which series is convergent.
a.
b.
____ 13. Find the values of p for which the series is convergent.
a.
b.
c.
d.
____ 14. Find the radius of convergence and the interval of convergence of the power series.
a.
b.
c.
d.
____ 15. Suppose that the radius of convergence of the power series is . What is the radius of
convergence of the power series .
a.
b.
c.
d.
e.